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Illustrating SAS, ASA, and SSS Congruence Postulates in Mathematics 8, Papers of Mathematics

University of Southeastern Philippines (USEP)Mathematics

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Republic of the Philippines
DEPARTMENT OF EDUCATION
Region XI
DIVISION OF DAVAO CITY
Davao City
DAVAO CITY NATIONAL HIGH SCHOOL
F. Torres St., Davao City
Telefax No. (082) 227 9102
LESSON PLAN
MATHEMATICS 8
Date: March 10, 2022
I. COMPETENCY:
Illustrates the SAS, ASA and SSS congruence postulates (M8GE-IIId-e-1)
II. OBJECTIVES: At the end of the lesson, the students are expected to:
A. define SAS, ASA, and SSS congruence postulates
B. illustrates the SAS, ASA, and SSS congruence postulates.
C. relate SAS, ASA, and SSS congruence postulates in real life situations.
III. SUBJECT MATTER:
A. Topic โ€“ Illustrating the SAS, ASA and SSS Congruence Postulates.
B. References: Mathematics 8 Quarter 3: Module 3
C. Materials: Laptop, Self-Learning Module, PowerPoint, Google Meet, WiFi,
sticks, protractor, ruler, paper, and art paper.
IV. PRELIMINARIES
1. Prayer
2. Checking of Attendance
3. Classroom Rules
V. LESSON PROPER
1. Activity/Motivation
โ€ข The teacher will give the students a review about the past lesson.
1. Given โˆ†DRY โ‰… โˆ†SOT, give the corresponding part congruent to each
given side or angle below.
1. ๐‘…๐ท
๏Œค
๏Œค
๏Œค
๏Œค
๏Œค
โ†” _______ 4. โˆ Y โ†” _______
2. ๐‘…๐‘Œ
๏Œค
๏Œค
๏Œค
๏Œค
โ†” _______ 5. โˆ O โ†” _______
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Republic of the Philippines DEPARTMENT OF EDUCATION Region XI

DIVISION OF DAVAO CITY

Davao City

DAVAO CITY NATIONAL HIGH SCHOOL

F. Torres St., Davao City Telefax No. (082) 227 9102 LESSON PLAN MATHEMATICS 8 Date: March 10 , 2022 I. COMPETENCY: Illustrates the SAS, ASA and SSS congruence postulates (M8GE-IIId-e-1) II. OBJECTIVES: At the end of the lesson, the students are expected to:

A. define SAS, ASA, and SSS congruence postulates

B. illustrates the SAS, ASA, and SSS congruence postulates.

C. relate SAS, ASA, and SSS congruence postulates in real life situations.

III. SUBJECT MATTER:

A. Topic โ€“ Illustrating the SAS, ASA and SSS Congruence Postulates. B. References: Mathematics 8 Quarter 3: Module 3 C. Materials: Laptop, Self-Learning Module, PowerPoint, Google Meet, WiFi, sticks, protractor, ruler, paper, and art paper. IV. PRELIMINARIES

  1. Prayer
  2. Checking of Attendance
  3. Classroom Rules V. LESSON PROPER
  4. Activity/Motivation
  • The teacher will give the students a review about the past lesson.
  1. Given โˆ†DRY โ‰… โˆ†SOT , give the corresponding part congruent to each given side or angle below.
  2. ๐‘…๐ท ฬ…ฬ…ฬ…ฬ…ฬ… โ†” _______ 4. โˆ Y โ†” _______
  3. ๐‘…๐‘Œฬ…ฬ…ฬ…ฬ… โ†” _______ 5. โˆ O โ†” _______

3. ๐‘†๐‘‡ฬ…ฬ…ฬ…ฬ… โ†” _______ 6. โˆ D โ†” _______

  1. Given โˆ†SET โ‰… โˆ†KEN , give all the corresponding congruent parts.
  2. _______________ 4. _______________
  3. _______________ 5. _______________
  4. _______________ 6. _______________
  • The teacher will give an activity for the new lesson. I. Consider the location map below. A. Identify the following places: 1. The corner between Lopez St. and Pablo St. 2. The corner between Pablo St. and Loyola St. 3. Loyola St. and Lopez St. B. Identify the street common to each places: 1. Paulโ€™s residence and the Municipal Hospital 2. Barangay Hall and Municipal Hospital 3. Barangay Hall and Paulโ€™s residence. II. Refer to the location map in the previous item, rename Paulโ€™s House as A , Barangay Hall as B and the Municipal Hospital as C.
  1. What is the name of the triangle formed?
  2. What are the vertices of the triangle?
  3. What are the sides of the triangle?
  4. What angle is between ฬ…๐ด๐ตฬ…ฬ…ฬ… and ๐ด๐ถฬ…ฬ…ฬ…ฬ…? between ๐ต๐ถฬ…ฬ…ฬ…ฬ… and ๐ถ๐ดฬ…ฬ…ฬ…ฬ…? between ๐ต๐ดฬ…ฬ…ฬ…ฬ… and ๐ต๐ถฬ…ฬ…ฬ…ฬ…?

TRIANGLE CONGRUENCE POSTULATES

  1. SAS (Side-Angle-Side) Congruence Postulate If two sides and an included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the triangles are congruent. To illustrate SAS congruence postulate. Students will do the activity below. To perform this, you need to prepare first the following:
  2. Materials needed: sticks, protractor, ruler, paper, art paper.
  3. Cut sticks into the following lengths:
    • 2 sticks 3 cm long - __________
    • 2 sticks 4 cm long - ______________
    • 2 sticks 5 cm long - __________________
  4. Measure 2 angles 90ยฐ, 2 angles of 54ยฐ, 2 angles of 36ยฐ on the corners of three colored pieces of art papers, cut them out and label them. Teacher will ask the students about the activity.

2. ASA (Angle-Side-Angle) Congruence Postulate If two angles and the included side of one triangle are congruent to the corresponding two angles and an included side of another triangle, then the triangles are congruent. Teacher will ask the students about the activity. In the activity above, given only two angles with included side in Triangle 1 with the same measure to the two angles and included side of Triangle 2, notice that the measures of the third angles of the triangles are equal and the lengths of the two remaining corresponding sides are also equal. With this, all the six corresponding parts are congruent. Thus, it can be concluded that two triangles are congruent although there are only three corresponding congruent parts (two angles and their included side).

Activity 2 Direction: Complete the congruence statement using the indicated congruence postulate.

1. SAS (Side-Angle-Side) Congruence Postulate 1. ๐›ฅ๐‘ƒ๐‘„๐‘… โ‰… _________ 2. ๐›ฅ๐‘†๐‘‡๐ฟ โ‰… __________ Questions: 1. What are the three corresponding congruent parts in item 1? in item 2? Name them. 2. When can you say that two triangles are congruent by SAS congruence postulate? 2: ASA (Angle-Side- Angle) Congruence Postulate 1. ๐›ฅVML โ‰… _________ 2. ๐›ฅLMN โ‰… _________ Questions: 1. What are the three corresponding congruent parts in item 1? in item 2? Name them. 2. When can you say that two triangles are congruent by ASA congruence postulate? 3: SSS (Side-Side-Side) Congruence Postulate 1. ๐›ฅACE โ‰… _________ 2. ๐›ฅCAB โ‰… _________

Questions:

  1. What are the three corresponding congruent parts in item 1? in item 2? Name them.

2. When can you say that two triangles are congruent by SSS

congruence postulate?

  1. Generalization A postulate is a statement, which is accepted as true without proof. to be true. For SSS (Side-Side-Side) Congruence Postulate , states that the two triangles are congruent if the three sides of the triangle are congruent to the corresponding three sides of the other triangle. In SAS (Side-Angle-Side) Congruence Postulate , states that the triangles are congruent if two sides and the included angle of the triangle are congruent to the corresponding two sides and the included angle of the other triangle. Note: Included angle is the angle between the two sides of a triangle. In ASA (Angle-Side- Angle) Congruence Postulate , states that the triangles are congruent if two angles and the included side are congruent to the corresponding two angles and the included side of the other triangle. Note: Included side is the side common to the two angles of a triangle. VI. EVALUATION/ASSIGNMENT Directions: Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper.
  2. Which of the illustration below represents the ASA Congruence Postulate?
  3. Which of the illustrations below represents the SAS Congruence Postulate?
  4. Given โˆ†LOT, what is the included angle between ๐ฟ๐‘‚ฬ…ฬ…ฬ…ฬ… and ๐‘‚๐‘‡ฬ…ฬ…ฬ…ฬ…?

A. โˆ L C. โˆ T

B. โˆ O D. โˆ TLO