8

Mathematics
Quarter 3 – Module 4:
Solves Corresponding Parts of
Congruent Triangles
Mathematics – Grade 8
Quarter 3 – Module 4: Solves Corresponding Parts of Congruent Triangles
First Edition, 2020

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Mathematics
Quarter 3 – Module 4:
Solves Corresponding Parts of
Congruent Triangles
Introductory Message
For the facilitator:
As a facilitator, you are expected to orient the learners on how to
use this module. You also need to keep track of the learners' progress
while allowing them to manage their own learning at home.
Furthermore, you are expected to encourage and assist the learners as
they do the tasks included in the module.

For the learner:

As a learner, you must learn to become responsible of your own
learning. Take time to read, understand, and perform the different
activities in the module.
As you go through the different activities of this module be
reminded of the following:
1. Use the module with care. Do not put unnecessary mark/s on any
part of the module. Use a separate sheet of paper in answering the
exercises.
2. Don’t forget to answer Let Us Try before moving on to the other
activities.
3. Read the instructions carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking
your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are done.
If you encounter any difficulty in answering the tasks in this
module, do not hesitate to consult your teacher or facilitator. Always
bear in mind that you are not alone. We hope that through this material,
you will experience meaningful learning and gain deep understanding
of the relevant competencies. You can do it!

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 Let Us Learn
You have learned in the previous lesson about illustrating the SAS, ASA,
and SSS congruence postulate. Now in this module you will learn how to solve
corresponding parts of congruent triangles (M8GE-IIIF-1). Let’s enjoy and have fun
in learning new lesson in this module.

Lesson- Solves corresponding parts of congruent triangles – M8GE-IIIf-1

Specifically, you will;

1. identify corresponding sides and angles of the two congruent triangles;

2. illustrate congruent triangle according to the given sides and angles; and
3. solve corresponding parts of congruent triangles.

Let Us Try
NAME ME!

Determine whether the sides or angles are corresponding sides, corresponding

angles, or neither of the given ∆𝐵𝐸𝐷 and ∆𝐶𝐴𝑅 below.

B C

E A
D R

__________________________1. ∠D and ∠R

__________________________2. ∠B and ∠A

__________________________3. ∠E and ∠A

__________________________4. ̅̅̅̅
𝑩𝑬 and ̅̅̅̅
𝑪𝑹

̅̅̅̅̅ and 𝑪𝑹
__________________________5. 𝑩𝑫 ̅̅̅̅

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 Let Us Study

Example 1.

Given that ABE ≅ DBC, name all corresponding parts.

B
E C

Solution: D

The correspondence of the vertices can be used to name the congruent sides and
angles of the two triangles.

Corresponding Sides Corresponding Angles

AB ≅ DB ∠A ≅ ∠D
BE ≅ BC ∠ABE ≅ ∠DBC
AB ≅ DB ∠E ≅ ∠C

Example 2.

O I 4 X
Given: ONE ≅ SIX, m∠E = 65, and IX = 4
Find:
a. m∠X
b. NE

65°
Solution: E N S

a. Since ∠X ≅ ∠E, you know that m∠X = m∠E = 65, therefore m∠X = 65.

b. Since NE ≅ IX, you know that NE = IX = 4, therefore NE = 4.

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Example 3:

Given: ABC ≅ CDE, AB = 36, BC = 28, AC = 43, and CE = 2x + 3.

a. Draw the congruent triangles and label the congruent parts
b. Find the value of x.

Solution: Some of the congruent triangles

a. Draw the congruent triangles and label the congruent parts.

A C
36

C 28
B D E

b. Since ABC ≅ CDE, then AC ≅ CE. Hence, AC = CE by the definition of

congruent segment.

AC = CE
43 = 2x + 3 → Subtract 3 from each side. Subtraction Property of Equality.

43 - 3 = 2x + 3 – 3

40 = 2x → Divide each side by 2 to get the value of x.

40 = 2x
2 2

20 = x

Checking: Substitute the value of x = 20 into the given equation to prove that
̅̅̅̅
𝐴𝐶 = ̅̅̅̅
𝐶𝐸 are equal.
AC = CE

43 = 2x + 3

43 = 2(20) + 3
43 = 40 + 3

43 = 43

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Example 4:

Given: PRY ≅ SLM, ̅̅̅̅

𝑅𝑌 = 14, ̅̅̅̅
𝑃𝑅 = 12, ̅̅̅̅
𝑃𝑌 = 9, and ̅̅̅̅
𝑆𝑀 = 2x – 1.
Find: The value of x.

Solution:
Since PRY ≅ SLM, then PR ≅ SL. Hence, PY = SM by the definition of congruent
segment.

PY = SM

9 = 2x – 1 → Add 1 from each side. Addition Property of Equality.

9 + 1 = 2x – 1 + 1

10 = 2x → Divide each side by 2 to get the value of x.

10 = 2x
2 2

5=x

Checking: Substitute the value of x =5 into the given equation to prove that
̅̅̅̅ ̅̅̅̅ are equal.
𝑃𝑌 = 𝑆𝑀

PY = SM
9 = 2x – 1

9 = 2(5) – 1

9 = 10 – 1
9=9

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 Let Us Practice
Identify all pairs of corresponding congruent parts of the given triangles.

R M A

U S E
Corresponding Sides Corresponding Angles

Let Us Practice More

A. Given: If ∆LMN ≅ ∆RST, m∠T = 25° and ̅̅̅̅

LN = 12cm.
̅̅̅̅.
Find the m∠S and RT

L M T
12 cm

N S R

B. Given: If JEM ≅ RAD, m∠A = 105° and ME = 10 cm. Find the m∠E and AD.
D
M

J E A R

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 Let Us Remember

Corresponding Parts of Congruent Triangles are Congruent.

Corresponding Angles
In a pair of similar triangles, the corresponding angles are the angles with the same
measure.

Corresponding Sides
In a pair of similar triangles, the corresponding sides are the sides with the same
measure.

If the corresponding sides are congruent and corresponding angles are

congruent, then the two triangles are congruent.

The sum measure of the interior angles of a triangle is 𝟏𝟖𝟎°.

Given the figure below ∆KSY ≅ ∆CIE. The corresponding sides and angles are
as follows:

Corresponding Angles Corresponding Sides

SK ≅ IC
∠S ≅ ∠I
SY ≅ EI
∠K ≅ ∠C
̅̅̅̅ ≅ EC
KY ̅̅̅̅
∠Y ≅ ∠E

Y E

K S I C

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 Let Us Assess

Multiple Choice. Choose the letter of the best answer.

1. The pair of polygons at the right is congruent. Which of the following statements
must be true? E
S
a. ∠D ≅ ∠R R
b. ∠E ≅ ∠S
c. ∠DE ≅ ∠RS D
d. EF ≅ RT
F T

For items 2-3: Refer on the figure below.

Given ∆EYZ ≅ ∆OCN, find the following:

2. If ∆EYZ ≅ ∆OCN then, ̅̅̅̅

EY ≅ _____.

a. ̅̅̅̅
𝑂𝑁 b. ̅̅̅̅
𝐶𝑁 c. ̅̅̅̅
𝐶𝑂 d. ̅̅̅̅
𝐸𝑌

3. If ∆EYZ ≅ ∆OCN then, what is the corresponding angle of ∠N?

a. ∠V b. ∠E c. ∠Y d. ∠C

4. If ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹, m∠A = 50, and m∠E = 30, what is m∠C?

a. 30 b. 50 c.100 d.130

5. If ∆ABC ≅ ∆QRS, m∠A = x – 10, and m∠Q = 2x – 30, what is m∠A?

a. 10 b. 20 c. 30 d.40

6. What is the length of side BC?

D B

3 6

` E F A C

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a. 2 units b. 4 units c. 6 units d. 8 units

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7. ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐹𝐺 as shown. Find 𝑥.

A E

600

450 𝑥

B C F G

a. 300 b. 400 c. 600 d. 750

For items 8 -9

Given ∆𝐵𝑂𝑋 ≅ ∆𝑃𝐼𝑁 , 𝑚∠𝑋 = 55, 𝑎𝑛𝑑 ̅̅̅

IN = 4. B P

8. What is the measure of ∠I?

a. 45° b. 35° c. 55° d. 90° 55°

X O N 4 I

9. What is the measure of ̅̅̅̅̅

OX?
a. 5 b. 4 c. 6 d. 8

̅̅̅̅ ≅ 𝑃𝑅
10. What is the value of x so that ∆ABC ≅ ∆𝑃𝑄𝑅 𝑖𝑓 𝐴𝐶 ̅̅̅̅ ?
B P x+10 R

C 20 A Q

a. 4 b. 7 c. 18 d. 10

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 Let Us Enhance
Imagine that you are an engineer, and you want to draw your own house.
Create your dream house using only triangles. Be creative and widen your
imagination. Give a brief explanation of your masterpiece.

Rubrics for Scoring

CRITERIA OUTSTANDING SATISFACTORY DEVELOPING BEGINNING
10 POINTS 8 POINTS 5 POINTS 2 POINTS
Explanation Explanation Explanation Explanation
shows through shows shows gaps shows illogical
Mathematical reasoning and substantial in reasoning reasoning
Reasoning insightful reasoning
justification
The output is The output is Most part of Some of
Accuracy correct and correct the output of details are
shown in the are correct
detail correct
The The The The
presentation is presentation is presentation presentation is
delivered in a delivered in a is delivered delivered in a
very clear manner. in clear manner.
Presentation convincing Appropriate disorganized It does not use
manner. visual materials manner. any visual
Appropriate used. Some visual materials.
and creative materials
visual used.
materials
used.

Let Us Reflect
I hope you have learned a lot form this lesson. Always put in mind that
triangle can only be congruent if their corresponding sides and corresponding angles
are congruent. You can apply it when you make your dream house real soon.

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Let Us Assess
Test I
1. D
2. C
3. A
4. C
5. B
6. C
7. D
8. C
9. B
10.D
Let Us Practice More Let Us Practice Let Us Try
A. m∠S = 65° Corresponding Sides 1. Corresponding Angle
̅̅̅̅
𝐿𝑁 ≅ 𝑅𝑇
̅̅̅̅= 12cm 𝑈𝑆 ̅̅̅̅̅
̅̅̅̅ ≅ 𝑀𝐴 2. Neither
̅̅̅̅ ̅̅̅̅̅
𝑅𝑈 ≅ 𝑀𝐸 3. Corresponding
B. m∠E = 105° 𝑅𝑆 ̅̅̅̅
̅̅̅̅ ≅ 𝐴𝐸 Angles
̅̅̅̅̅ ≅ 𝐴𝐷
𝑀𝐸 ̅̅̅̅ = 10𝑐𝑚 4. Neither
Corresponding Angles 5. Corresponding Sides
∠R ≅ ∠E
∠S ≅ ∠A
∠U ≅ ∠M
Answer Key
 References

Orlando A. Oronce,Marilyn O. Mendoza, E- Math Worktext in

Mathematics 8 Revised Edition: Manila, Philippines, Rex Book
Store, 2019, 254 – 260.

“Similar Triangles in Geometry,” kris taking math.

www.kristakingmath.com/blog/similar-triangles-in-geometry

“Prentice Hall Geometry, “Pearson Education, Inc.,

www.anderson.k12.ky.us/downloads/notebook2.pdf

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Elpidio Quirino Ave., Poblacion District, Davao City, 8000 Davao del Sur

Telefax: (082) 224-3274, (082) 222-1672

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