Mathematics 7 Quarter 3 Module 7: Construct Triangles, Squares, Rectangles, Regular Pentagons, and Regular Hexagons

Mathematics Quarter 3 – Module 7: Construct Triangles, Squares, Rectangles, Regular Pentagons, and Regular Hexagons

7

Mathematics

Quarter 3 – Module 7:

Construct Triangles, Squares, Rectangles, Regular Pentagons, and Regular Hexagons

[illustration: students reading and studying outdoors and at a desk, a teacher at a table, and a boy working by lantern light beside a globe]

Mathematics – Grade 7 Alternative Delivery Mode Quarter 3 – Module 7: Construct triangles, squares, rectangles, regular pentagons, and regular hexagons. First Edition, 2020

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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

Printed in the Philippines by ___________________________

Development Team of the Module

Writer: Jenypete O. Diana Illustrator: Ian Caesar E. Frondoza Layout Artist: James B. De Los Reyes Management Team: Allan G. Farnazo, Gilbert B. Barrera, Arturo D. Tingson Jr, Peter Van C. Ang-ug, Donna S. Panes, Elizabeth G. Torres, Judith B. Alba

Department of Education – SOCCSKSARGEN – Region XII

Office Address: Regional Center, Brgy. Carpenter Hill, City of Koronadal Telefax: (083) 2288825/ (083) 2281893 E-mail Address: region12@deped.gov.ph

7

Mathematics

Quarter 3 – Module 7:

Construct Triangles, Squares, Rectangles, Regular Pentagons, and Regular Hexagons

Introductory Message

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.

Thank you.

What I Need to Know

[illustration: hand touching a touchscreen, icon beside the heading]

This module was designed and written with you in mind. It is here to help you learn triangles, squares, rectangles, regular pentagons, and regular hexagons. The scope of this module can be used in many different learning situations. The language used recognizes your vocabulary level. The lessons were arranged to follow the standard sequence in the curriculum guide. But the order in which you read them can be adjust to correspond with the textbook you are now using.

The module is comprised of only one lesson:

• Constructing Triangles, Squares, Rectangles, Regular Pentagons, and Regular Hexagons

After going through this module, you are expected to:

1. Perform polygon constructions such as triangles, squares, rectangles, regular pentagons, and regular hexagons using straightedge and drawing compass.
2. Draw an object that shows the shape of a triangle, square, rectangle, regular pentagon, and regular hexagon.

What I Know

[illustration: hand holding a pencil, icon beside the heading]

Choose the letter with the best answer. Write your answer on a separate sheet of paper.

1. What do you call a drawing tool that can be used to draw circles?
   a. Compass
   b. Pencil
   c. Protractor
   d. Straightedge

   
   

2. It is a step-by-step process used to draw accurate geometric figures.
   a. Construction
   b. Drawing
   c. Outline
   d. Sketch

   
   

3. Anything that allows you to produce a straight line but not able to measure distances.
   a. Compass
   b. Pencil
   c. Protractor
   d. Straightedge

   
   

4. How to start constructing a square?
   a. Draw perpendicular lines.
   b. It starts by connecting the four points.
   c. It starts with the given line side.
   d. Measure the diagonal lines.

   
   

5. How do you know if you construct a rectangle accurately?
   a. If it has four right angles and two equal diagonals.
   b. If the sides are equal.
   c. If it has four sides.
   d. If it has two perpendicular lines.

   
   

6. In constructing △ ABC with AB = 4cm, BC = 5cm and AC = 6cm, which of the following is a correct order of steps in constructing a triangle?
   a. Step 1: Draw a line AB, 4cm long.
   Step 2: Draw an arc of radius 5cm with B as the center.
   Step 3: Draw an arc of radius 6cm with A as the center to cut the arc drawn in Step 2 at C.
   Step 4: Join C, the point of intersection of the two arcs to the point A and

   
   

   b. Step 1: Draw a line AB, 4cm long.
   Step 2: Join C, the point of intersection of the two arcs to the point A and B.
   Step 3: Draw an arc of radius 6cm with A as the center to cut the arc drawn in Step 2 at C.
   Step 4: Draw an arc of radius 5cm with B as the center.

   
   

   c. Step 1: Draw an arc of radius 5cm with B as the center.
   Step 2: Join C, the point of intersection of the two arcs to the point A and B.
   Step 3: Draw an arc of radius 6cm with A as the center to cut the arc drawn in Step 2 at C.
   Step 4: Draw a line AB, 4cm long.

   
   

   d. Step 1: Draw an arc of radius 5cm with B as the center.
   Step 2: Join C, the point of intersection of the two arcs to the point A and B.
   Step 3: Draw a line AB, 4cm long.
   Step 4: Draw an arc of radius 6cm with A as the center to cut the arc drawn in Step 2 at C.

   
   

7. What are the sides of hexagon FAMILY?

   
   

[illustration: hexagon with vertices labeled M, I, A, L, Y, F; M at top left, I at top right, A at left, L at right, F at bottom left, Y at bottom right]

a. FA, AM, MI, IL, LY, YF b. FA, YL, LA, AM, MI, IL c. FY, MI, AL, YL, AF, AM d. MI, AL, FY, YF, LA, IM

2. Which of the following figure of square with side equal to 1.5cm?

   
   

   a. [illustration: square]
   b. [illustration: square]
   c. [illustration: square]
   d. [illustration: square]

   
   

3. Construct Pentagon LOVED.
   Which of the following is a correct order of steps in constructing a pentagon?

   
   

   a. Step 1: Draw diameter LM on a circle G.
   Step 2: Construct a perpendicular to LM at G and intersecting the circle at N.
   Step 3: Draw the perpendicular bisector of NG creating its midpoint P.
   Step 4: Circle P with radius NP.
   Step 5: Draw MP intersecting circle P at Q and R.
   Step 6: With the compass on M and radius MR, draw an arc intersecting the larger circle at E and V.
   Step 7: With compass on M, and radius MQ, draw an arc intersecting the larger circle at D and O.
   Step 8: Connect L and D, L and O, O and V, V and E, and, E and D to form the sides of LD, LO, OV, VE, ED of the regular pentagon LOVED.

   
   

   b. Step 1: Draw diameter LM on a circle G.
   Step 2: Draw the perpendicular bisector of NG creating its midpoint P.
   Step 3: Construct a perpendicular to LM at G and intersecting the circle at N.
   Step 4: Circle P with radius NP.
   Step 5: Draw MP intersecting circle P at Q and R.
   Step 6: With compass on M, and radius MQ, draw an arc intersecting the larger circle at D and O.
   Step 7: With the compass on M and radius MR, draw an arc intersecting the larger circle at E and V.
   Step 8: Connect L and D, L and O, O and V, V and E, and, E and D to form the sides of LD, LO, OV, VE, ED of the regular pentagon LOVED.

   
   

   c. Step 1: Circle P with radius NP.
   Step 2: Construct a perpendicular to LM at G and intersecting the circle at N.
   Step 3: Draw the perpendicular bisector of NG creating its midpoint P.
   Step 4: Draw diameter LM on a Circle G.
   Step 5: Draw MP intersecting circle P at Q and R.
   Step 6: With the compass on M and radius MR, draw an arc intersecting the larger circle at E and V.
   Step 7: With compass on M, and radius MQ, draw an arc intersecting the larger circle at D and O.
   Step 8: Connect L and D, L and O, O and V, V and E, and, E and D to form the sides of LD, LO, OV, VE, ED of the regular pentagon LOVED.

   
   

   d. Step 1: Circle P with radius NP.
   Step 2: Draw the perpendicular bisector of NG creating its midpoint P.
   Step 3: Construct a perpendicular to LM at G and intersecting the circle at N.
   Step 4: Draw diameter LM on a Circle G.

   
   

Step 5: Draw MP intersecting circle P at Q and R. Step 6: With the compass on M and radius MR, draw an arc intersecting the larger circle at E and V. Step 7: With compass on M, and radius MQ, draw an arc intersecting the larger circle at D and O. Step 8: Connect L and D, L and O, O and V, V and E, and, E and D to form the sides of LD, LO, OV, VE, ED of the regular pentagon LOVED.

4. Which of the following rectangles measures 1.5cm and by 2.5cm?

A. [illustration: rectangle, choice A]

B. [illustration: rectangle, choice B]

C. [illustration: rectangle, choice C]

D. [illustration: rectangle, choice D]

For item 11-15,using a ruler and a compass construct the following:

11. Rectangular door whose length measures 5cm and width measures 3cm.
12. A picture of square Sponge Bob whose side measures 2.7cm.
13. Triangular ruler whose side measures 2.5cm
14. A pentagon serving tray whose side measures 1.2cm
15. Hexagonal clock whose side measures 3cm.

Lesson 1: Construct Triangles, Squares, Rectangles, Regular Pentagons, and Regular Hexagons

In the previous lesson, you have learned the convexity, angles and sides of polygons. Do you know that fashion designers, builders, architects, engineers and carpenters use drawings to communicate their ideas to others?

What’s In

Let’s review!

Construct Me!

At the end of the activity you will be able to construct basic construction in geometry.

1. Construct line segment CJ congruent to a given segment RS.
   [illustration: line segment with endpoints marked, labeled RS]

   
   

2. Construct angle C congruent to a given angle J.
   [illustration: angle labeled J]

   
   

3. Construct Ray JA⃗ such that A is in the interior of ∠KJL and ∠KJA = ∠AJL with the given angle J.
   [illustration: angle J with points K and L and ray through A]

   
   

4. Locate the midpoint U of SN and construct the perpendicular bisector of SN.
   [illustration: segment with endpoints S and N]

   
   

5. Construct a line through C perpendicular to ℓ.
   Given: Line ℓ and point C on ℓ

   
   

6. Construct a line through C perpendicular to ℓ.
   Given: Line ℓ and point C which is not on ℓ.

   
   

7. Construct a line through C parallel to ℓ.
   Given: Line ℓ and point C not on ℓ.

   
   

What’s New

Polygons such as triangles, squares, rectangles, pentagons and hexagons are all around us. If you look around your room, you see these shapes in most of the objects. In mathematics, we try to understand and create these shapes. We can create these shapes by constructing them outside or inside of another object.

Observe the figures below.

[illustration: regular pentagon inscribed in a circle, with a 108° interior angle and a 72° central angle marked; Figure 2] [illustration: regular hexagon with vertices labeled A to F and center O; Figure 3] [illustration: square inscribed in a circle with points P1 to P8 and center O, titled “square construction”; Figure 1]

1. In the figures above, name all the polygons.
2. How many triangles formed in pentagon?
3. In figure 3, how many squares are there?

What is It

Using a compass and straightedge, we can construct polygons. We use a straightedge to construct a line, ray, or segment when two points are given. The marks indicated in the ruler may not be used for measurement. We use a compass to construct an arc (part of a circle) or a circle, and a radius length.

Construct a triangle with sides measures a, b, c.

1. Given segments whose lengths are a, b, and c
   [illustration: three horizontal segments labeled c, b, and a]

   
   

2. Draw AD⃗. Place the point of the compass on A and make its opening equal to c intersecting AD⃗ at B.
   AB = c
   [illustration: ray from A through B to D, with an arc at B]

   
   

3. With the point of the compass still on A, make its opening equal to b and draw an arc.
   [illustration: ray with points A, c, B, D and an arc above A]

   
   

4. Place the point of the compass on B and make its opening equal to a. Draw an arc intersecting the arc in step 3 at point C.
   [illustration: ray with points A, c, B, D, and point C where two arcs meet]

   
   

5. Connect the points A and C and points B and C.
   △ABC with AB = c
   AC = b
   BC = a
   [illustration: triangle ABC with sides c, b, and a]

   
   

Construct a triangle whose sides measure a, b, c and the included angle, <A.

1. Given: 2 segments whose lengths area, b, and the included angle, <A.
   [illustration: segments labeled c and b, and angle at point A]

   
   

2. Copy <A. Let the sides of the angle be AM and AN.
   [illustration: angle at A with sides AM and AN]

   
   

3. With the compass point on A, make the width of the compass equal to c and make an arc on AM. Mark the point B.
   [illustration: angle at A with arc marked c crossing AM at B]

   
   

4. With the compass point still on A, make the width of the compass equal to b and make an arc on AN. Mark the point C.
   [illustration: angle at A with arc marked b on AN at point C]

   
   

5. Connect B and C to form △BC
   [illustration: triangle A, B, C with sides b and c marked]

   
   

Constructing of a Square

1. Draw a line segment MN. Let this be aside of the square.
   [illustration: line segment with endpoints M and N]

   
   

2. Extend segment MN. Using a compass, mark two arcs from N on the line. Mark the points as F and G.
   [illustration: line with points F, N, G and two intersecting arcs]

   
   

3. Name the point where the arcs meet as point C. Then points N and C
   [illustration: line with points M, F, N, G, and perpendicular line through N ending at C]

   
   

4. Set the length of the compass to 4 cm and mark arc from point M and N. The point where the arc intersects NC is the vertex O of the square.
   [illustration: line M, F, N, G with perpendicular line through N and point O]

   
   

5. With length of 4 cm on the compass, mark an arc from the point O and point M. Mark their point of intersection as point P.
   [illustration: two perpendicular lines at M and N with arcs marking points P and O]

   
   

6. Connect points O and P as well as M and P to have MNOP□
   [illustration: square with vertices P, O, M, N]

   
   

Constructing of a Rectangle

1. Draw line segment m.
   [illustration: horizontal line segment labeled m]

   
   

2. Put two points A and B to make a segment AB on line segment m.
   [illustration: line m with points A and B]

   
   

3. Construct two perpendicular segments. Using a compass, mark two arcs on the line A and another two arcs on line B.
   [illustration: line m with perpendicular lines and arcs at points A and B]

   
   

4. Mark off congruent sides and label the vertices as point C and D.
   [illustration: line m with perpendicular lines at A and B and points C and D]

   
   

5. Connect point C and D to form □ ABCD.
   [illustration: rectangle ABCD with arcs at the vertices]

   
   

6. The four interior angles should be right angles and the diagonals should be equal.
   [illustration: rectangle ABCD with right-angle marks and both diagonals drawn]

   
   

Constructing of a Pentagon

1. Draw diameter LM on ⊙ O.
   [illustration: circle with center O and diameter LM, point L at the top]

   
   

2. Construct a perpendicular to LM at O and intersecting the circle at N.
   [illustration: circle with center O, horizontal line through N and O]

   
   

3. Draw the perpendicular bisector of NO creating its midpoint P.
   [illustration: circle with center O, point N on the left, midpoint P, and point M on the lower arc]

   
   

4. ⊙ P with radius NP.
   [illustration: circle centered at P passing through N and O, with a larger circle and points N, P, O, and M]

   
   

5. Draw $\overline{NP}$ intersecting circle P at Q and R.

   
   

[illustration: construction of a pentagon, step 5, showing NP intersecting the small circle at Q and R]

6. With the compass on M and radius $\overline{MR}$ draw an arc intersecting the larger circle at S and T.

[illustration: construction of a pentagon, step 6, showing an arc from M intersecting the larger circle at S and T]

7. With the compass on M and radius $\overline{MQ}$, draw an arc intersecting the larger circle at U and V.

[illustration: construction of a pentagon, step 7, showing an arc from M intersecting the larger circle at U and V]

8. Connect L and U, L and V, V and T, T and S, and S and U, to form the sides of $\overline{LU}$, $\overline{LV}$, $\overline{VT}$, $\overline{TS}$, $\overline{SU}$ of the regular pentagon LVTSU.

[illustration: completed regular pentagon LVTSU inside the circle]

Construction of a Hexagon

1. Let $\overline{LM}$ be a side of the hexagon. Set the width of the compass equate to LM.

[illustration: segment LM with a compass set to its width]

2. With $\overline{LM}$ as the width of the compass and the compass point at L, draw an arc above LM.

[illustration: arc drawn above LM from point L]

3. With the same width of the compass and the compass point at M, draw an arc above LM intersecting the arc in step 2 at N.

[illustration: arcs from L and M meeting at N]

4. With the same width of the compass and the compass point at N, draw ○ N.

[illustration: circle centered at N passing through L and M]

5. With LM as the width and the compass point at A, draw an arc intersecting the circle at P. This is the third vertex of the regular hexagon.

[illustration: arc from A intersecting the circle at P]

6. With LM as the width and the compass point at P, draw an arc intersecting the circle O. This is the fourth vertex of the regular hexagon.

[illustration: arc from P intersecting the circle at O]

6. Configure in this manner until you have vertices Q and R.

[illustration: circle with vertices L, M, P, Q, R, and S marked]

7. Connect the vertices.

[illustration: hexagon formed by connecting the vertices, with N at the center]

8. Done. The result is a regular hexagon LPQRSM.

[illustration: completed regular hexagon LPQRSM with center N]

What’s More

Try it!

Construct the following polygons in a separate sheet of paper.

1. Construct the triangle given the following:
   a. three segments whose length are d, e, and f.

[illustration: three line segments labeled d, e, and f]

b. sides d and e and the included angle, <A.

[illustration: segments d and e and angle A]

2-4. Construct a square, regular pentagon, and a regular hexagon with side equal to 1.5 inch.

4. Construct a rectangle with length 1.5inch and width 1inch.

What I Have Learned

Here is another activity that will let you apply what you have learned about constructing triangle, square, regular pentagon and hexagon. Choose the word/expressions from the box to fill in each blank to make a statement true. Write your answer on a separate sheet of paper.

arc	line segment
circle	perpendicular bisector
connect	perpendicular line
diameter	rectangle
intersecting	vertices

1. In constructing a triangle, draw $\overrightarrow{AD}$. Place the compass on A and make its opening equal to c _____ AD at B.
2. For the last step in constructing a triangle, _____ the points A and C, and points B and C.
3. In constructing a square, you draw a _____ as the side of the square.
4. In step 3 in constructing a square, draw an _____ intersecting the perpendicular line.
5. Draw a _____ on a circle as the first step in n constructing a regular pentagon.
6. In step 3 constructing a regular pentagon, draw the _____ to create a midpoint.
7. In making a regular hexagon, with the same width of the compass and the compass point at C, draw a _____.
8. Connect the _____ to form a regular hexagon.
9. In constructing a rectangle, you need to draw two _____.
10. What do you call a polygon with four right angles and two diagonals?

What I Can Do

Apply what you have learned about constructing triangle, square, rectangle, regular pentagon and hexagon.

Construct the following in a separate sheet of paper.

1. A triangle whose sides have lengths 1.5cm, 2cm, and 2.5cm.
2. A triangle whose sides have lengths 2.5cm and 3cm with an included angle of 30º.
3. A square whose sides equal to 2.3cm+.
4. A rectangle whose length is equal to 3cm and width equal to 2.5cm.
5. A regular pentagon whose side equal to 2.7cm.
6. A regular hexagon whose sides equal to 3.5cm.

Assessment

Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.

1. What do you call a step-by-step process used to create accurate geometric figures?
   A. Construction
   B. Drawing
   C. Outline
   D. Sketch

   
   

2. How to begin in constructing a square?
   A. Draw perpendicular lines.
   B. It starts by connecting the four points.
   C. It starts with given side.
   D. Measure the diagonal lines.

   
   

3. Construct △ABC with AB = 3cm, BC= 4cm and AC= 5cm. Which of the following is a correct order of steps in constructing a triangle?

   
   

   A. Step 1: Draw a line AB, 3cm long.
   Step 2: Draw an arc of radius 4cm with B as the center.
   Step 3: Draw an arc of radius 5cm with A as the center to cut the arc drawn in Step 2 at C.
   Step 4: Join C, the point of intersection of the two arcs to the point A and B.

   
   

   B. Step 1: Draw a line AB, 3cm long.
   Step 2: Join C, the point of intersection of the two arcs to the point A and B.
   Step 3: Draw an arc of radius 5cm with A as the center to cut the arc drawn in Step 2 at C.
   Step 4: Draw an arc of radius 4cm with B as the center.

   
   

   C. Step 1: Draw an arc of radius 4cm with B as the center.
   Step 2: Join C, the point of intersection of the two arcs to the point A and B.
   Step 3: Draw an arc of radius 5cm with A as the center to cut the arc drawn in Step 2 at C.
   Step 4: Draw a line AB, 3cm long.

   
   

   D. Step 1: Draw an arc of radius 4cm with B as the center.
   Step 2: Join C, the point of intersection of the two arcs to the point A and B.
   Step 3: Draw a line AB, 3cm long.
   Step 4: Draw an arc of radius 6cm with A as the center to cut the arc drawn in Step 2 at C.

   
   

4. It is a drawing tool that can be used to draw circle and its parts, and duplicate lengths?
   A. Compass
   B. Pencil
   C. Protractor
   D. Straightedge

   
   

5. What do you call that allows you to produce a straight line but not able to measure distances?
   A. Compass
   B. Pencil
   C. Protractor
   D. Straightedge

   
   

6. How do you know if you construct a square accurately?
   A. If it has two right angles and two equal diagonals.
   B. If all sides are equal and parallel.
   C. If it has four sides.
   D. If it has two perpendicular lines.

   
   

7. What are the sides of hexagon COUPLE?

   
   

[chart: hexagon diagram with vertices labeled U (top left), P (top right), L (right), E (bottom right), C (bottom left), O (left)]

A. $\overline{CE}$, $\overline{CO}$, $\overline{OL}$, $\overline{OU}$, $\overline{UP}$, $\overline{PL}$ B. $\overline{CO}$, $\overline{OU}$, $\overline{UP}$, $\overline{PL}$, $\overline{LE}$, $\overline{EC}$ C. $\overline{UP}$, $\overline{OL}$, $\overline{CE}$, $\overline{EL}$, $\overline{LP}$, $\overline{CO}$ D. $\overline{UC}$, $\overline{PE}$, $\overline{LO}$, $\overline{CE}$, $\overline{UP}$, $\overline{OL}$

8. Which of the following construction of rectangle with sides equal to 1.8cm and 2.3cm?

A. [illustration: rectangle] B. [illustration: rectangle] C. [illustration: rectangle] D. [illustration: rectangle]

9. Construct Pentagon BRAVE. Which of the following is a correct order of steps in constructing a pentagon?

   
   

   A. Step 1: Draw diameter $\overline{CJ}$ on a Circle D.
   Step 2: Draw the perpendicular bisector of $\overline{FD}$ creating its midpoint G.
   Step 3: Draw $\overline{JG}$ intersecting circle G at Hand I.
   Step 4: Construct a perpendicular to $\overline{CJ}$ at D and intersecting the circle at F.
   Step 5: Circle G with radius $\overline{FG}$.
   Step 6: With compass on J, and radius $\overline{JH}$, draw an arc intersecting the larger circle at E and R.
   Step 7: With the compass on J and radius $\overline{JI}$, draw an arc intersecting the larger circle at V and A.
   Step 8: Connect B and E, B and R, R and A, A and V, and, V and E to form the sides of $\overline{BE}$, $\overline{BR}$, $\overline{RA}$, $\overline{AV}$, $\overline{VE}$ of the regular pentagon BRAVE.

   
   

   B. Step 1: Draw diameter $\overline{CJ}$ on a Circle D.
   Step 2: Construct a perpendicular to $\overline{CJ}$ at D and intersecting the circle at F.
   Step 3: Draw the perpendicular bisector of $\overline{FD}$ creating its midpoint G.
   Step 4: Circle G with radius $\overline{FG}$.
   Step 5: Draw $\overline{JG}$ intersecting circle G at Hand I.
   Step 6: With the compass on J and radius $\overline{JI}$, draw an arc intersecting the larger circle at V and A.
   Step 7: With compass on J, and radius $\overline{JH}$, draw an arc intersecting the larger circle at E and R.

   
   

   Step 8: Connect B and E, B and R, R and A, A and V, and, V and E to form the sides of $\overline{BE}$, $\overline{BR}$, $\overline{RA}$, $\overline{AV}$, $\overline{VE}$ of the regular pentagon BRAVE.

   
   

   C. Step 3: Draw the perpendicular bisector of $\overline{FD}$ creating its midpoint G.
   Step 1: Draw diameter $\overline{CJ}$ on a Circle D.
   Step 5: Draw $\overline{JG}$ intersecting circle G at Hand I.
   Step 2: Construct a perpendicular to $\overline{CJ}$ at D and intersecting the circle at F.
   Step 4: Circle G with radius $\overline{FG}$.
   Step 6: With the compass on J and radius $\overline{JI}$, draw an arc intersecting the larger circle at V and A.
   Step 7: With compass on J, and radius $\overline{JH}$, draw an arc intersecting the larger circle at E and R.
   Step 8: Connect B and E, B and R, R and A, A and V, and, V and E to form the sides of $\overline{BE}$, $\overline{BR}$, $\overline{RA}$, $\overline{AV}$, $\overline{VE}$ of the regular pentagon BRAVE.

   
   

   D. Step 1: Circle G with radius $\overline{FG}$.
   Step 2: Draw diameter $\overline{CJ}$ on a Circle D.
   Step 3: Construct a perpendicular to $\overline{CJ}$ at D and intersecting the circle at F.
   Step 4: Draw the perpendicular bisector of $\overline{FD}$ creating its midpoint G.
   Step 5: Draw $\overline{JG}$ intersecting circle G at Hand I.
   Step 6: With compass on J, and radius $\overline{JH}$, draw an arc intersecting the larger circle at E and R.
   Step 7: With the compass on J and radius $\overline{JI}$, draw an arc intersecting the larger circle at V and A.
   Step 9: Connect B and E, B and R, R and A, A and V, and, V and E to form the sides of $\overline{BE}$, $\overline{BR}$, $\overline{RA}$, $\overline{AV}$, $\overline{VE}$ of the regular pentagon BRAVE.

   
   

10. What are the sides of pentagon LEARN?

    
    

[chart: pentagon diagram with vertices labeled L (top), E (right), A (bottom right), R (bottom left), N (left)]

A. $\overline{LN}$, $\overline{LE}$, $\overline{LR}$, $\overline{LA}$, $\overline{RA}$ B. $\overline{LR}$, $\overline{LA}$, $\overline{NA}$, $\overline{NE}$, $\overline{RE}$ C. $\overline{LN}$, $\overline{LE}$, $\overline{EA}$, $\overline{AR}$, $\overline{RN}$ D. $\overline{LN}$, $\overline{NE}$, $\overline{EA}$, $\overline{AR}$, $\overline{RN}$

For item 11-15, construct the following:

11. A curtain whose length measures 6cm and width measures 8cm.
12. A flat screen TV whose side measures 7cm.
13. Triangular frame whose side measures 2.5cm
14. A pentagon ashtray whose side measures 1.2cm
15. Hexagonal mirror whose side measures 3cm.

Additional Activities

This segment includes supplementary activities related to construction of a polygon.

Look at your surroundings and observe everything. In a long bond paper, draw an object that shows the shape of:

1. Triangle
2. Square
3. Rectangle
4. Regular pentagon
5. Regular hexagon.

Make it attractive and creative.

Answer Key

[transcriber’s note: this page is printed upside down; the content is transcribed in reading order]

What’s In

1. [illustration: line with points J and C and arrowheads at both ends]
2. [illustration: angle with vertex C, points B and A, and an arc marked]
3. [illustration: point J with lines to K and A, arc marked at J, and an arrow]
4. [illustration: line N–S with point U, perpendicular lines marked with x and y]
5. [illustration: horizontal line f with points B, C, A, and a perpendicular line]
6. [illustration: lines f and perpendicular line with points B, A, and C]
7. [illustration: lines f, n, and m with point C and right-angle marks]

What I Know

1. A
2. A
3. D
4. C
5. A
6. A
7. A
8. C
9. A
10. B

11-15. Students’ answer may vary depending on how the students construct/draw the object. But the measurement must be in accordance with the given.

What’s New

1. 3 Squares
2. 4 Triangles
3. Triangle, Square, Rectangle, Pentagon, Hexagon

What I Have Learned

1. intersecting
2. connect
3. line segment
4. arc
5. diameter
6. perpendicular bisector
7. circle
8. vertices
9. perpendicular line
10. rectangle

What I Can Do

1. [illustration: triangle pointing downward]
2. [illustration: triangle pointing downward]
3. [illustration: square]
4. [illustration: rectangle, partly visible at top left]
5. [illustration: regular pentagon]
6. [illustration: regular hexagon]

[transcriber’s note: this page is printed upside down; the content is transcribed in reading order]

Assessment

11-15. Students’ answer may vary depending on how the students construct/draw the object. But the measurement must be in accordance with the given.

1. A
2. C
3. A
4. A
5. D
6. A
7. B
8. C
9. B
10. C

Additional Activities

1-5. Students’ answer may vary depending on how the students construct/draw the object. But the measurement must be in accordance with the given.

References

Mathematics –Grade 7 Learner’s Material First Edition, 2013 ISBN: 978-971-9990-60-4

Oronce, Orlando A., et.al, E-Math I Elementary Algebra Revised Edition 2010. Rex Book Store, Inc.

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