Mathematics 8 Quarter 3 Module 3: Illustrating Triangle Congruence

Mathematics Quarter 3 – Module 3 Illustrating Triangle Congruence

[illustration: group of students studying outdoors and indoors with a teacher, a globe, and a lamp]

Mathematics – Grade 8 Alternative Delivery Mode Quarter 3 – Module 3: Illustrating Triangle Congruence First Edition, 2020

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Development Team of the Module

Writer: Rochelle Anna Myla A. Paronda,

Language Editor: Joel B. Asonto

Content Editors: Victorino Nimes, Myracell Buenaflor, Marie Grace O. Aparre, Ella C. Armayan

Reviewers: Rhea J. Yparraguirre, Villaflor D. Edillor, Shirley C. Compe, Imelda B. Llasos, Caren L. Alamin, Jayrold Virtudazo Navarra, Alma R. Velaasco

Illustrator: Fritch A. Paronda

Layout Artists: Fritch A. Paronda, James B. De Los Reyes

Management Team: Francis Cesar B. Bringas, Isidro M. Biol, Jr., Maripaz F. Magno, Josephine Chonie M. Obseñares, Josita B. Carmen, Celsa A. Casa, Regina Euann A. Puerto, Bryan L. Arreo, Elnie Anthony P. Barcena, Leopardo P. Cortes, Jr., Claire Ann P. Gonzaga

Mathematics Quarter 3 – Module 3 Illustrating Triangle Congruence

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 circle icon, part-title icon]

This module was designed and written with you in mind. It is here to help you illustrate triangle congruence. You are provided with varied activities to process the knowledge and skills learned and to deepen and transfer your understanding of the lesson. The scope of this module enables you to use it in many different learning situations. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.

This module contains concepts on how to illustrate triangle congruence.

After going through this module, you are expected to:

1. define triangle congruence;
2. draw and label the corresponding parts of two congruent triangles;
3. identify corresponding parts of two congruent triangles; and
4. relate triangle congruence in real-life.

What I Know

[illustration: hand holding a pencil, part-title icon]

Directions: Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper.

1. Which of the following is a symbol used for congruence?
   a. =
   b. ≠
   c. ≈
   d. ≅

   
   

2. How many pairs of corresponding congruent angles are there in two congruent triangles?
   a. 1
   b. 2
   c. 3
   d. 4

   
   

3. Which of the symbols below is used to indicate correspondence?
   a. ≅
   b. ∠
   c. Δ
   d. ↔

   
   

4. Which of the following statements best describe congruent triangles?
   I. They are similar.
   II. They have the same size.
   III. They have the same shape.
   IV. They are equilateral triangles.
   a. I only
   b. III only
   c. III and IV together
   d. II and III together

   
   

5. How many pairs of corresponding sides are there in two congruent triangles?
   a. 1
   b. 2
   c. 3
   d. 4

   
   

6. Which of the following statements best describe the corresponding parts of congruent triangles?
   a. They are not equal.
   b. They are congruent.
   c. They are supplementary.
   d. They are complementary.

   
   

For items 7 – 10, consider the figure below.

[illustration: two triangles sharing vertex A, labeled M, N, A, C, T, with tick marks and angle arcs showing congruent parts]

7. Which segment corresponds to $\overline{NT}$?
   a. $\overline{AT}$
   b. $\overline{AC}$
   c. $\overline{CM}$
   d. $\overline{MA}$

   
   

8. Which angle corresponds to ∠T?
   a. ∠A
   b. ∠C
   c. ∠M
   d. ∠N

   
   

9. Which vertex corresponds to A?
   a. A
   b. M
   c. N
   d. T

   
   

10. What conclusion can you make in the figure?
    a. ΔANT ≅ ΔMAC
    b. ΔANT ≅ ΔCAM
    c. ΔAMC ≅ ΔATN
    d. ΔAMC ≅ ΔTAN

    
    

11. If ΔLMN ≅ ΔPRQ, then what angle corresponds to ∠Q?
    a. ∠L
    b. ∠N
    c. ∠P
    d. ∠R

    
    

12. Which of the following figures illustrate pair of congruent triangles?
    a. [illustration: two triangles meeting at a point C, with vertices A, B, D, E]
    b. [illustration: two triangles with vertices P, R, O, Q, S]
    c. [illustration: parallelogram-like figure with vertices A, B, C, D and a diagonal, with tick marks]
    d. [illustration: triangle with vertices U, T, V, W and a perpendicular segment from U to V, with a right-angle mark]

    
    

13. Which of the following correspondence is equivalent to ∠JKL ≅ ∠MNO?
    a. ∠KJL ↔ ∠MON
    b. ∠KJL ↔ ∠OMN
    c. ∠JLK ↔ ∠NMO
    d. ∠LKJ ↔ ∠ONM

    
    

14. If ΔNAT ≅ ΔGEO, then name the corresponding sides of the congruent triangles.
    a. $\overline{NA} \cong \overline{GE}$; $\overline{AT} \cong \overline{EO}$; $\overline{NT} \cong \overline{GO}$
    b. $\overline{NA} \cong \overline{GO}$; $\overline{AT} \cong \overline{EO}$; $\overline{NT} \cong \overline{GE}$
    c. $\overline{AT} \cong \overline{EO}$; $\overline{NT} \cong \overline{EG}$; $\overline{NA} \cong \overline{OG}$
    d. $\overline{AT} \cong \overline{GE}$; $\overline{NA} \cong \overline{EO}$; $\overline{NT} \cong \overline{GO}$

    
    

15. Lyka was asked by her Math teacher to give and write the corresponding sides of congruent triangles, ΔCAT and ΔDOG, on the board. Her answer is shown below.

    
    

    $\overline{AC} \leftrightarrow \overline{OD}$
    $\overline{CT} \leftrightarrow \overline{DG}$
    $\overline{AT} \leftrightarrow \overline{OD}$

    
    

    Is Lyka’s answer correct?
    a. Yes, because each side of ΔCAT is paired correctly to each side of ΔDOG.
    b. Yes, because each angle of ΔCAT is paired correctly to each angle of ΔDOG.
    c. No, because $\overline{AT}$ corresponds to $\overline{OG}$.
    d. No, because $\overline{CT}$ corresponds to $\overline{OG}$.

    
    

[transcriber’s note: the supplied pages are printed pages 5 to 12 of the module, numbered 9 to 16 here as requested]

Lesson 1: Illustrating Triangle Congruence

Designs and patterns having the same size and shape thrive in almost every place. These can be seen in bridges and condominiums, furniture and appliances, as well as in fabrics and crafts.

Triangle is one of the most important figures studied in Mathematics because of its many uses in the real-world.

Let us know more about triangles, particularly congruent triangles by performing the array of activities in this module. Have fun!

What’s In

[illustration: hand holding a jigsaw puzzle piece]

Activity: Identify V-A-S (Vertices – Angles – Sides)

Directions: Identify the vertices, angles, and sides of each triangle. Then, answer the questions below using complete sentences.

[illustration: triangle with vertices labeled A, B, and C]

Vertices	Angles	Sides

[illustration: triangle with vertices labeled Q, R, and S]

Vertices	Angles	Sides

Questions:

1. How did you identify the vertices, angles, and sides of each triangle?
2. How would you define angle?
3. What about the definition of a vertex?
4. In geometry, what is meant by side?

What’s New

[illustration: hand holding a seedling sprouting from a leaf]

Activity: Four Pics – Two Words

Directions: Consider the figures below and answer the questions that follow.

[illustration: roof truss frame with triangular sections]

[illustration: kite with triangular sections]

[illustration: sailboat with triangular sail and hull]

[illustration: bridge truss with triangular panels on three supports]

Questions

1. What geometric figures were highlighted in the illustrations?
2. What have you observed with the size and shape of the geometric figures? Explain your answer.

What is It

[illustration: magnifying glass held by a hand]

• Two line segments are congruent if their endpoints can be made to coincide.
• Two angles are congruent if their sides can be made to coincide.
• Two triangles are equal if they have the same size and shape.
• Two triangles are congruent if their corresponding parts are congruent.

Definition of Correspondence

Pairing the parts of one group to the parts of another group is called correspondence. Correspondence uses the notation “↔”.

[illustration: triangle with vertices labeled A, N, and T, beside a triangle with vertices labeled E, G, and O]

Assume $\Delta NAT$ coincides with $\Delta GEO$, such that the vertices of $\Delta NAT$ fit exactly over the vertices of $\Delta GEO$. The correspondence can be created between triangles.

[chart: correspondence arrows; ΔNAT ↔ ΔGEO]

ΔNAT ↔ ΔGEO

Note

In naming congruent triangles, the order of the letters representing the vertices of one triangle shall be written in the same order as their corresponding vertices in the other triangle.

In this correspondence, there are three pairs of corresponding vertices, angles, and sides.

Corresponding Vertices	Corresponding Angles	Corresponding Sides
N ↔ G A ↔ E T ↔ O	∠N ↔ ∠G ∠A ↔ ∠E ∠T ↔ ∠O	$\overline{NA}$ ↔ $\overline{GE}$ $\overline{AT}$ ↔ $\overline{EO}$ $\overline{NT}$ ↔ $\overline{GO}$

Since the vertices of ΔNAT fit exactly with the vertices of ΔGEO, therefore ΔNAT and ΔGEO are congruent. In symbols,

ΔNAT ≅ ΔGEO

Definition of Congruent Triangles

Two triangles are congruent if and only if the corresponding sides and the corresponding angles are congruent.

(ΔNAT ≅ ΔGEO is read as “triangle N − A − T is congruent to triangle G − E − O”)

It implies that the corresponding parts of congruent triangles are also congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent.

Congruent Angles	Congruent Sides
∠N ≅ ∠G ∠A ≅ ∠E ∠T ≅ ∠O	$\overline{NA}$ ≅ $\overline{GE}$ $\overline{AT}$ ≅ $\overline{EO}$ $\overline{NT}$ ≅ $\overline{GO}$

Conversely, if the corresponding parts of the two triangles are congruent, then the two triangles are congruent.

Example 1

ΔCAT ≅ ΔDOG. Write down the pairs of corresponding parts.

[illustration: triangle CAT and triangle DOG with tick marks and angle arcs marking congruent parts]

Solution

The congruent parts of congruent triangles can be determined with the help of arcs and tick-marks.

Corresponding Angles	Corresponding Sides
∠C ↔ ∠D ∠A ↔ ∠O ∠T ↔ ∠G	$\overline{CA}$ ↔ $\overline{DO}$ $\overline{CT}$ ↔ $\overline{DG}$ $\overline{AT}$ ↔ $\overline{OG}$

Example 2

Given that the two triangles below are congruent, list the pairs of congruent angles and congruent sides and then name the congruent triangles.

[illustration: triangle PSA and triangle NSO sharing vertex S, with tick marks and angle arcs]

Solution

Congruent Angles	Congruent Sides
∠A ≅ ∠O ∠P ≅ ∠N ∠PSA ≅ ∠NSO	$\overline{PS}$ ≅ $\overline{NS}$ $\overline{PA}$ ≅ $\overline{NO}$ $\overline{SA}$ ≅ $\overline{SO}$

ΔPSA ≅ ΔNSO

Example 3

Consider ΔFAE ≅ ΔTEA. List down the pairs of congruent angles and congruent sides.

[illustration: parallelogram-shaped figure with vertices E, T, A, and F, with tick marks and angle arcs]

Solution

Again, the congruent parts of congruent triangles can be determined with the help of arcs and tick-marks. Since ΔFAE ≅ ΔTEA, then the corresponding parts are as follows:

Corresponding Angles	Corresponding Sides
∠F ↔ ∠T ∠FEA ↔ ∠TAE ∠FAE ↔ ∠TEA	$\overline{FA}$ ↔ $\overline{TE}$ $\overline{FE}$ ↔ $\overline{TA}$ $\overline{EA}$ ↔ $\overline{AE}$

Example 4

Assume that segments and angles in the numbered triangles are congruent. Identify which triangles are congruent.

[illustration: roof truss with numbered triangles 1 to 6]

Solution

Looking at the figures, it can be deduced that Δ1 ≅ Δ6, Δ2 ≅ Δ5, and Δ3 ≅ Δ4.

Remember:

• Triangles that have exactly the same size and shape are congruent.
• Two triangles are congruent if their corresponding sides and angles are congruent.
• Two triangles are congruent if they fit exactly or coincide when one triangle is put on top of the other.

What’s More

[illustration: hand stacking three blocks]

Activity 1: Find My PARTner

Description: In this activity, you will be pairing parts of one triangle to the parts of another triangle. Note that the notation “↔” shows corresponding parts.

Directions: Copy the table on your answer sheet and supply the missing part of the triangle that will make each correspondence complete. Answer the questions that follow.

[illustration: triangle ABC and triangle DEF with tick marks and angle arcs]

Corresponding Vertices	Corresponding Angles	Corresponding Sides
A ↔ ↔ E C ↔ F	∠A ↔ _____ ∠B ↔ _____ ∠C ↔ _____	$\overline{AB}$ ↔ ↔ $\overline{DF}$ $\overline{BC}$ ↔ _____

Questions:

1. What have you noticed on the given triangles?
2. What does the mark of the angles and sides of the triangle indicate?
3. Are there angles and sides that have the same measure and length? Explain your answer.
4. Describe the relationship between ΔABC and ΔDEF.

Activity 2: Draw and Name

Directions: Do what is asked. Use a separate sheet of paper.

1. Draw ΔACT ≅ ΔNOW. Put identical markings on corresponding congruent parts.

[blank answer box]

2. ΔSTR ≅ ΔRAS. Name the six pairs of corresponding congruent parts.

[illustration: triangles STR and RAS sharing side RS, with vertices T and A above and R and S below]

Congruent Angles	Congruent Sides

3. Listed below are the six pairs of corresponding parts of two congruent triangles. Name the two congruent triangles.

Congruent Angles	Congruent Sides
∠T ≅ ∠E ∠O ≅ ∠O ∠W ≅ ∠N	$\overline{TW}$ ≅ $\overline{EN}$ $\overline{OT}$ ≅ $\overline{OE}$ $\overline{WO}$ ≅ $\overline{NO}$

Congruent Triangles

What I Have Learned

Let us see how far you have learned about congruent triangles by answering each question in the diagram below. Consider the figure at the center. Write your answers on a separate paper.

[chart: flowchart; hexagon diagram “What I Have Learned”]

1. What are the corresponding vertices?
2. What are the corresponding angles?
3. What are the corresponding sides?
4. What are the congruent angles?
5. What are the congruent sides?
6. What are the congruent triangles?

Center figure: [illustration: two triangles meeting at point M, with congruence markings; labels E, R, C, O, M]

What I Can Do

One of the structural applications of triangles can be seen in bridges. In the illustration below, there are pairs of congruent triangles. Do what is asked below and write your answer on a separate paper.

[illustration: bridge with pairs of congruent triangles]

Directions:

1. Select a pair of congruent triangles.
2. Label these triangles as Δ𝑆𝐴𝐹 and Δ𝐸𝐴𝐹.
3. Put similar markings to show clearly the congruent sides and congruent angles.
4. List down the corresponding congruent parts of the congruent triangles.

Assessment

Directions: Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper.

1. Which of the following statements is not true about congruent triangles?
   a. They are dissimilar.
   b. They are coinciding.
   c. They have the same size and shape.
   d. They have corresponding congruent parts.

   
   

2. How many pairs of corresponding congruent parts are there in two congruent triangles?
   a. 2 c. 4
   b. 3 d. 6

   
   

3. If Δ𝐹𝑅𝑌 ≅ Δ𝐻𝑂𝑇, which segment is congruent to 𝑅𝑌̅̅̅̅?
   a. 𝐻𝑇̅̅̅̅ c. 𝑂𝑇̅̅̅̅
   b. 𝐹𝑌̅̅̅̅ d. 𝑅𝐹̅̅̅̅

   
   

4. Which of the following is true about the corresponding parts of congruent triangles?
   a. They are unequal.
   b. They are congruent.
   c. They are supplementary.
   d. They are complementary.

   
   

5. If Δ𝑆𝐼𝑇 ≅ Δ𝐻𝑂𝑃, then what angle corresponds to ∠𝑇?
   a. ∠𝐻 c. ∠𝑃
   b. ∠𝐼 d. ∠𝑆

   
   

6. Name the congruent triangles whose pairs of corresponding parts are shown below.

   
   

∠𝐻 ≅ ∠𝑆 𝑅𝐸̅̅̅̅ ≅ 𝑁𝑂̅̅̅̅ ∠𝑅 ≅ ∠𝑁 𝐻𝐸̅̅̅̅ ≅ 𝑆𝑂̅̅̅̅ ∠𝐸 ≅ ∠𝑂 𝐻𝑅̅̅̅̅ ≅ 𝑆𝑁̅̅̅̅

a. Δ𝑁𝑂𝑆 ≅ Δ𝐻𝐸𝑅 c. Δ𝑆𝑂𝑁 ≅ Δ𝐸𝐻𝑅 b. Δ𝑁𝑆𝑂 ≅ Δ𝐸𝑅𝐻 d. Δ𝑆𝑂𝑁 ≅ Δ𝐻𝐸𝑅

7. In the figure, Δ𝐶𝑅𝑌 ≅ Δ𝑂𝐵𝑆, what is the side corresponding to 𝑆𝐵̅̅̅ ?

[illustration: triangle CRY and triangle OBS with congruence markings; labels C, R, Y, O, B, S]

a. 𝐵𝐶̅̅̅̅ b. 𝐶𝑅̅̅̅̅ c. 𝑌𝐶̅̅̅̅ d. 𝑌𝑅̅̅̅̅

8. Use the marked triangles in writing a correct congruence statement.

[illustration: two marked triangles; labels T, R, A, O, Y, C]

a. 𝐶𝑅̅̅̅̅ ≅ 𝑇𝑌̅̅̅̅ 𝑂𝑌̅̅̅̅ ≅ 𝐶𝐴̅̅̅̅ 𝑅𝐴̅̅̅̅ ≅ 𝑂𝑌̅̅̅̅ Δ𝑇𝑂𝑌 ≅ Δ𝐶𝐴𝑅

b. 𝐶𝑅̅̅̅̅ ≅ 𝑇𝑌̅̅̅̅ 𝑂𝑌̅̅̅̅ ≅ 𝐴𝑅̅̅̅̅ 𝑇𝑌̅̅̅̅ ≅ 𝑅𝐴̅̅̅̅ Δ𝑇𝑂𝑌 ≅ Δ𝐶𝐴𝑅

c. 𝑇𝑂̅̅̅̅ ≅ 𝐶𝐴̅̅̅̅ 𝑇𝑌̅̅̅̅ ≅ 𝑅𝐶̅̅̅̅ 𝑂𝑌̅̅̅̅ ≅ 𝐴𝐶̅̅̅̅ Δ𝑇𝑂𝑌 ≅ Δ𝐶𝐴𝑅

d. 𝑂𝑇̅̅̅̅ ≅ 𝐴𝐶̅̅̅̅ 𝑇𝑌̅̅̅̅ ≅ 𝐶𝑅̅̅̅̅ 𝑂𝑌̅̅̅̅ ≅ 𝐴𝑅̅̅̅̅ Δ𝑇𝑂𝑌 ≅ Δ𝐶𝐴𝑅

For items 9-12, refer to the figure shown below.

[illustration: triangle IFE with point V on base FE; segment IV marked as perpendicular to FE; labels I, F, V, E]

9. Which of the following shows a pair of congruent triangles?
   a. Δ𝐹𝐼𝑉 ≅ Δ𝐼𝑉𝐸 c. Δ𝐼𝐹𝑉 ≅ Δ𝐼𝑉𝐸
   b. Δ𝐹𝐼𝑉 ≅ Δ𝐸𝐼𝑉 d. Δ𝐼𝐹𝑉 ≅ Δ𝑉𝐼𝐸

   
   

10. What angle corresponds to ∠𝐹𝑉𝐼?
    a. ∠𝐸 c. ∠𝐸𝐼𝑉
    b. ∠𝐹 d. ∠𝐸𝑉𝐼

    
    

11. Which segment is congruent to 𝐸𝑉̅̅̅̅?
    a. 𝐼𝐸̅̅̅ c. 𝐹𝑉̅̅̅̅
    b. 𝐼𝑉̅̅̅ d. 𝑉𝐸̅̅̅̅

    
    

12. Which vertex corresponds to 𝐹?
    a. 𝐸 c. 𝐹
    b. 𝐼 d. 𝑉

    
    

13. Which of the following figures show congruent triangles?

    
    

[illustration: four figures; A: two triangles meeting at C with labels A, B, C, D, E; B: triangles TUV and OCW with labels T, U, V, O, C, W; C: triangles OPQ and QRS with labels O, P, Q, R, S; D: triangle LOE with altitude OV and labels L, O, V, E]

a. (A)  c. (C)
b. (B)  d. (D)

14. What would be the name of the congruent triangles given their corresponding sides: 𝐿𝑂̅̅̅ ≅ 𝑅𝑃̅̅̅̅, 𝑀𝑂̅̅̅̅̅ ≅ 𝑄𝑃̅̅̅̅, 𝐿𝑀̅̅̅ ≅ 𝑅𝑄̅̅̅̅?
    a. Δ𝐿𝑂𝑀 ≅ Δ𝑄𝑃𝑅 c. Δ𝑀𝑂𝐿 ≅ Δ𝑅𝑄𝑃
    b. Δ𝑂𝑀𝐿 ≅ Δ𝑃𝑄𝑅 d. Δ𝐿𝑀𝑂 ≅ Δ𝑃𝑄𝑅

    
    

15. Which of the following illustrations below best describe the congruent triangle in item 14?

    
    

[illustration: four figures; A: triangles MOL and QPR; B: quadrilateral-like figure with triangles LMO and QRP, with congruence markings; C: triangles LMO and PRQ with angle markings; D: triangles MLO and QRP with congruence markings]

a. (A)  c. (C)
b. (B)  d. (D)

Additional Activities

Directions: Do what is asked. Use separate paper to draw your answers.

Given: Δ𝑅𝐸𝐷 ≅ Δ𝐸𝑅𝐴

[illustration: triangle W with points D and A on its sides and segments drawn from R to A and from E to D; labels W, D, A, R, E]

1. Separate the overlapping triangles.

[transcriber’s note: empty answer box for the response]

2. Put identical/similar markings to show clearly the congruent sides and congruent angles.

[transcriber’s note: empty answer box for the response]

Answer Key

[transcriber’s note: this page is printed rotated 180 degrees. The sections below are given in the order of the table, and each answer is followed by its printed number, as in the original.]

What’s New

1. Triangles
2. The triangles have the same size and shape.
3. If we put these triangles one over the other, they would fit exactly or coincide.

What’s In

For Δ𝐴𝐵𝐶 Vertices: A, B, C Angles: ∠𝐴, ∠𝐵, ∠𝐶 Sides: 𝐵𝐶̅̅̅̅, 𝐴𝐶̅̅̅̅, 𝐴𝐵̅̅̅̅

For Δ𝑄𝑅𝑆 Vertices: Q, R, S Angles: ∠𝑆, ∠𝑅, ∠𝑄 Sides: 𝑅𝑆̅̅̅̅, 𝑄𝑆̅̅̅̅, 𝑄𝑅̅̅̅̅

Angle – A pair of rays that have a common endpoint, provided that the rays do not lie on the line.

Vertex – In an angle, it is the common endpoint of two rays. In a polygon, it is the common endpoint of two sides.

Sides – In an angle, the sides are rays that form the angle. In a polygon, the sides are the segments that form a polygon.

What I Know

1. D
2. C
3. D
4. D
5. C
6. B
7. C
8. C
9. A
10. C
11. B
12. C
13. D
14. A
15. C

What’s More

Corresponding Vertices 𝐷 ↔ 𝐴 𝐸 ↔ 𝐵 1.

Corresponding Angles 𝐷∠ ↔ 𝐴∠ 𝐸∠ ↔ 𝐵∠ 𝐹∠ ↔ 𝐶∠

Corresponding Sides 𝐷𝐸̅̅̅̅ ↔ 𝐴𝐵̅̅̅̅ 𝐷𝐹̅̅̅̅ ↔ 𝐴𝐶̅̅̅̅ 𝐸𝐹̅̅̅̅ ↔ 𝐵𝐶̅̅̅̅

Note: Illustration varies however the congruent parts must be considered. 2.

Congruent Angles 𝑅∠ ≅ 𝑆∠ 𝐴∠ ≅ 𝑇∠ 𝑆∠ ≅ 𝑅∠ 3.

Congruent Sides 𝑅𝐴̅̅̅̅ ≅ 𝑆𝑇̅̅̅̅ 𝐴𝑆̅̅̅̅ ≅ 𝑇𝑅̅̅̅̅ 𝑅𝑆̅̅̅̅ ≅ 𝑆𝑅̅̅̅

Δ𝐸𝑂𝑁 ≅ Δ𝑇𝑂𝑊 [?] 4.

What I Have Learned

Δ𝑀𝑂𝐶 ≅ Δ𝑀𝐸𝑅 1. 𝑀 ↔ 𝑀 2. ∠𝑀 ↔ ∠𝑀 3. 𝑀𝐸̅̅̅̅̅ ↔ 𝑀𝑂̅̅̅̅̅ 4. ∠𝑀 ≅ ∠𝑀 5. 𝑀𝐸̅̅̅̅̅ ≅ 𝑀𝑂̅̅̅̅̅ 6.

What I Can Do

Congruent Angles Congruent Sides

𝑅 ↔ 𝐶 𝐸 ↔ 𝑂 𝑅∠ ↔ 𝐶∠ 𝐸∠ ↔ 𝑂∠ 𝑅𝐸̅̅̅̅ ↔ 𝐶𝑂̅̅̅̅ 𝑅𝑀̅̅̅̅̅ ↔ 𝐶𝑀̅̅̅̅̅ 𝑅∠ ≅ 𝐶∠ 𝐸∠ ≅ 𝑂∠ 𝑅𝐸̅̅̅̅ ≅ 𝐶𝑂̅̅̅̅ 𝑅𝑀̅̅̅̅̅ ≅ 𝐶𝑀̅̅̅̅̅

[illustration: triangle E, F, S, A with congruence markings]

∠𝐴 ≅ ∠𝐴 ∠𝐹 ≅ ∠𝐹 ∠𝐸 ≅ ∠𝑆 𝐴𝐸̅̅̅̅ ≅ 𝐴𝑆̅̅̅̅ 𝐸𝐹̅̅̅̅ ≅ 𝑆𝐹̅̅̅̅ 𝐴𝐹̅̅̅̅ ≅ 𝐴𝐹̅̅̅̅

Assessment

1. A
2. D
3. C
4. B
5. C
6. D
7. D
8. D
9. B
10. D
11. C
12. A
13. D
14. B
15. D

Additional Activities

[illustration: two triangles with congruence markings; labels partly illegible]

References

Abuzo, Emmanuel P., Bryant, Merden L., Cabrella, Jem Boy B. Caldez, Belen P., Callanta, Melvin M., Castro, Anastacia Preserfina I., Halabaso, Alicia R., Javier, Sonia P., Nocom, Roger T., and Ternida, Conception S. (2013). Grade 8 Mathematics Learners Module. pp. 352-353. Philippines. Book Media Press, Inc. and Printwell, Inc.

Bernabe, Julieta G., et.al. (2009). Revised Edition Geometry, pp. 88-90, Gregoria Araneta Avenue, Quezon City, Philippines. SD Publications, Inc.

Orines, Fernando B., et.al. (2008). Second Edition Next Century Mathematics, pp. 201-203, Quezon Avenue, Quezon City, Philippines. Phoenix Publishing House, Inc.

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