Math8 Quarter 3 Week 4 Triangle Congruence Postulates PDF

NAME:__________________________________________ 8 GRADE/SECTION:______________________________ MATHEMATICS Quarter III – Week 4 Triangle Congruence Postulates CONTEXTUALIZED LEARNING ACTIVITY SHEETS SCHOOLS DIVISIO...

NAME:__________________________________________ 8 GRADE/SECTION:______________________________ MATHEMATICS Quarter III – Week 4 Triangle Congruence Postulates CONTEXTUALIZED LEARNING ACTIVITY SHEETS SCHOOLS DIVISION OF PUERTO PRINCESA CITY Mathematics – Grade 8 Contextualized Learning Activity Sheets (CLAS) Quarter III - Week 4: Triangle Congruence Postulates First Edition, 2020 Republic Act 8293, Section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for the exploitation of such work for a profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this CLAS are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Schools Division of Puerto Princesa City Development Team of the Contextualized Learning Activity Sheets Writer: Charlene May C. Gavan Content Editor: Evelyn C. Silvestre Language Editor: Angelyn M. Aborot Proofreader: Irene M. Villamor Reviewers: Marie Vic C. Velasco PhD, Haydee C. Hitosis, Evelyn C. Silvestre, Joseph D. Aurello, Maricar T. Caliwag Illustrator: Pedro C. Rodriguez Jr. Layout Artist: Shiela Mae O. Salibio Management Team: Servillano A. Arzaga, CESO V, SDS Loida P. Adornado, PhD, ASDS Cyril C. Serador, PhD, CID Chief Ronald S. Brillantes, EPS-LRMS Manager Marie Vic C. Velasco, PhD, EPS-Mathematics Eva Joyce C. Presto, PDO II Rhea Ann A. Navilla, Librarian II Division Quality Assurance Team: Ronald S. Brillantes, Warly I. Salido, Haydee C. Hitosis, Joseph D. Aurello, Maricar T. Caliwag, Miguelito D. Campillos Meguilito D. Campillos Division of Puerto Princesa City-Learning Resource Management Section (LRMS) Sta. Monica Heights, Brgy. Sta. Monica, Puerto Princesa City Telephone No.: (048) 434 9438 Email Address: [email protected]  Lesson 1 Triangle Congruence Postulates MELC: Illustrates the SAS, ASA, and SSS congruence postulates M8GE-IIId-e-1 Objectives: 1. Recall the definition of triangle congruence. 2. State the SAS, ASA and SSS congruence postulates. 3. Illustrate the SAS, ASA and SSS congruence postulates. Let’s Try Directions: Read each item carefully. Write the letter of the correct answer on the space provided before each number. ______1. In ∆DOS, what side is included between ∠𝐷 and ∠𝑂? ̅̅̅̅ A. 𝐷𝑂 B. ̅̅̅̅ 𝐷𝑆 Figure 1 ̅̅̅̅ C. 𝑆𝐷 ̅̅̅̅ D. 𝑆𝑂 ______2. Consider ∆DOS in Figure 1. What angle is included between ̅̅̅̅ 𝐷𝑆 and ̅̅̅̅ 𝑆𝑂? A. ∠𝐷 B. ∠𝑂 C. ∠𝑆 D. ∠𝑆𝐷𝑂 ______3. Which is the correct congruence statements for the marked triangles? ̅̅̅̅ ≅ A. 𝐿𝑇 ̅̅̅̅, 𝐿𝑂 𝑀𝑆 ̅̅̅̅ ≅ ̅̅̅̅̅ ̅̅̅̅ ≅ 𝑀𝐸 , 𝑂𝑇 ̅̅̅̅, ∆LOT ≅ ∆MES 𝐸𝑆 B. ̅𝐿𝑇 ̅̅̅ ≅ ̅̅̅̅ 𝑆𝑀, ̅̅̅̅ 𝐿𝑂 ≅ 𝑀𝐸 , ̅̅̅̅ ̅̅̅̅̅ 𝑂𝑇 ≅ ̅̅̅̅ 𝐸𝑆, ∆LOT ≅ ∆SME ̅ C. 𝐿𝑇̅̅̅ ≅ ̅̅̅̅ 𝑀𝑆, ̅̅̅̅ 𝑂𝐿 ≅ 𝑀𝐸 , ̅̅̅̅ ̅̅̅̅̅ 𝑂𝑇 ≅ ̅̅̅̅ 𝑆𝐸, ∆LOT ≅ ∆MSE ̅̅̅̅ ≅ D. 𝑇𝐿 ̅̅̅̅, 𝐿𝑂 𝑀𝑆 ̅̅̅̅ ≅ ̅̅̅̅̅ ̅̅̅̅ ≅ 𝑀𝐸 , 𝑂𝑇 ̅̅̅̅̅ 𝑀𝐸 , ∆TOL ≅ ∆SME ______4. Which of the following statements is TRUE about SSS Congruence Postulate? A. If three sides of a triangle are congruent respectively to the three angles of another triangle, then the triangles are congruent. B. If three sides of a triangle are congruent to the three sides of another triangle, then the triangles are congruent. C. If three angles of a triangle are congruent to the three sides of another triangle, then the triangles are congruent. D. If three angles of a triangle are congruent to the three angles of another triangle, then the triangles are congruent. ______5. What Congruence Postulate is defined by the statement, “If two sides and an included angle of one triangle are congruent respectively to two sides and an included angle of another triangle, then the triangles are congruent”? A. ASA B. SAS C. AAS D. SSS ______6. Miguel knows that in ∆MIG and ∆JAN, 𝑀𝐼 = 𝐽𝐴, 𝐼𝐺 = 𝐴𝑁, 𝑎𝑛𝑑 𝑀𝐺 = 𝐽𝑁. Which postulate or theorem can he use to illustrate that the triangles are congruent? A. ASA B. SAS C. AAS D. SSS 1 ______7. In the given figure, corresponding congruent parts are marked. What must be the additional corresponding parts to make the triangles congruent by ASA Congruence Postulate? A D A. ∠𝐵 ≅ ∠𝐸 B. ∠𝐶 ≅ ∠𝐹 ̅̅̅̅ ≅ 𝐷𝐸 C. 𝐴𝐵 ̅̅̅̅ ̅̅̅̅ D. 𝐶𝐵 ≅ ̅̅̅̅ 𝐹𝐸 B C F E ______8. Which postulate or theorem can be used to prove that the triangles in the figure on the right are congruent? A. ASA C. AAS B. SAS D. SSS ______9. Which postulate or theorem can be used to prove that the triangles in the figure on the right are congruent? A. ASA C. AAS B. SAS D. SSS ______10. Which of the following illustrate the ASA congruence postulate? A. C. B. D. (Source: Emmanuel P. Abuzo et al., Mathematics 8: Learner’s Module, Pasig City: DepEd-IMCS, 2013, 345-348.) 2  Let’s Explore and Discover Unlocking Recall that for two triangles to be congruent, their of Difficulties corresponding sides and their corresponding angles must be congruent. In the given example below, ∆ABC ≅ ∆DEF. Included angle- is the angle between two sides of the triangle. Corresponding Angles Corresponding Sides ∠A ≅ ∠D ̅̅̅̅ ≅ 𝐷𝐸 𝐴𝐵 ̅̅̅̅ Included side- is ∠B ≅ ∠E ̅̅̅̅ 𝐵𝐶 ≅ ̅̅̅̅ 𝐸𝐹 the side common to two angles of a ∠C ≅ ∠F ̅̅̅̅ 𝐴𝐶 ≅ ̅̅̅̅ 𝐷𝐹 triangle. (Source: Julieta G. Bernabe.,Cecile M. De Leon, and Soledad Jose-Dilao. Geometry, Textbook for Third Year,Pilot Edition DepEd-IMCS, 2002, 94.) Now, consider some ways by which two triangles can be shown to be congruent, given less number of corresponding congruent parts. Triangle Congruence Postulates SAS (Side-Angle-Side) Congruence Postulate If two sides and an included angle of one triangle are congruent to the corresponding two sides and an included angle of another triangle, then the triangles are congruent. ̅̅̅̅̅ ≅ 𝑇𝐼 Corresponding sides: 𝑀𝐴 ̅̅̅ Corresponding included angles: ∠M ≅ ∠T ̅̅̅̅̅ ≅ 𝑇𝑁 Corresponding sides: 𝑀𝑅 ̅̅̅̅ Therefore, ∆MAR ≅ ∆TIN by SAS Congruence Postulate. Illustrative examples: S: ̅̅̅̅ 𝐴𝐵 ≅ ̅̅̅̅ 𝐷𝐸 S: ̅̅̅̅ 𝐴𝐶 ≅ ̅̅̅ 𝐸𝐽 A: ∠B ≅ ∠E A: ∠C ≅ ∠J S: ̅̅̅̅ 𝐵𝐶 ≅ ̅̅̅̅ 𝐸𝐹 S: ̅̅̅̅ 𝑅𝐶 ≅ ̅̅̅ 𝑇𝐽 1. 2. 3 ASA (Angle-Side-Angle) Congruence Postulate If two angles and an included side of one triangle are congruent to the corresponding two angles and an included side of another triangle, then the triangles are congruent. Corresponding angles:∠A ≅ ∠E Corresponding included sides: , ̅̅̅ 𝐽𝐴 ≅ ̅̅̅̅̅ 𝑀𝐸 Corresponding angles: ∠J ≅ ∠M Therefore, ∆JAY ≅ ∆MEL by ASA Congruence Postulate. Illustrative examples: A: ∠A ≅ ∠E A: ∠M ≅ ∠G S: ̅̅̅̅ 𝐴𝐶 ≅ ̅̅̅̅ 𝐸𝐷 ̅̅̅̅̅ ≅ 𝐺𝑉 S: 𝑀𝐴 ̅̅̅̅ A: ∠C ≅ ∠D A: ∠A ≅ ∠V 1. 2. SSS (Side-Side-Side) Congruence Postulate If three side of a triangle are congruent to the three side of another triangle, then the triangles are congruent. Corresponding sides: ̅̅̅̅ 𝐸𝐶 ≅ ̅̅̅̅ 𝐵𝑃 Corresponding sides: ̅̅̅̅ 𝐸𝑆 ≅ ̅̅̅ 𝐵𝐽 ̅̅̅̅ ≅ 𝑃𝐽 Corresponding sides: 𝐶𝑆 ̅̅̅ Therefore, ∆ESC ≅ ∆BJP by SSS Congruence Postulate. Illustrative examples: S: ̅̅̅̅ 𝐺𝐴 ≅ ̅̅̅̅ 𝑃𝑁 S: 𝐵𝐼 ≅ ̅̅̅̅ ̅̅̅ 𝐹𝐴 ̅̅̅ ≅ 𝐴𝑇 ̅̅̅̅ S: ̅̅̅̅ 𝐴𝐵 ≅ ̅̅̅̅ 𝑁𝐺 S: 𝐼𝐺 ̅̅̅̅ S: ̅̅̅̅ 𝐺𝐵 ≅ ̅̅̅̅ 𝑃𝐺 1. S: 𝐵𝐺 ≅ 𝐹𝑇̅ 2. (Source: Emmanuel P. Abuzo et al., Mathematics 8: Learner’s Module, Pasig City: DepEd-IMCS, 2013, 353-357.) 4  Let’s Practice Directions: Determine whether triangles are congruent using SAS, ASA, and SSS Congruence Postulates. Write your answer on the space provided in each number. 1. 4. _________________ _________________ 2. 5. _________________ _________________ 3. _________________ Directions: Complete the congruence statement using the indicated congruence postulate. 1. ∆BIG ≅ ∆_________ by SSS 3. ∆MAY ≅ ∆_______ by ASA 2. ∆CAR ≅ ∆_______ by SAS 4. ∆GAB ≅ ∆_______ by SSS When are two triangles congruent using SAS Congruence Postulate? ASA Congruence Postulates? and SSS Congruence Postulate?_____________________________________________ ________________________________________________________________________________________ 5  Let’s Do More Directions: Corresponding congruent parts are marked. Indicate the additional corresponding parts to make the triangles congruent using the specified Congruence Postulate for each number. Circle the letter of the correct answer. A. ∠𝐴 ≅ ∠D C. ∠𝐵 ≅ ∠E ASA: B. ∠𝐶 ≅ ∠F D. ∠𝐴𝐵𝐶 ≅ ∠DEF A. ∠𝐿 ≅ ∠P C. ∠𝐿𝑁𝑀 ≅ ∠PNO SAS: B. ∠𝑂 ≅ ∠M D. ∠𝑁𝑀𝐿 ≅ ∠NOP A. ̅̅̅̅ 𝐻𝑂 ≅ ̅̅̅̅ 𝑃𝐸 C. ̅̅̅̅ 𝐻𝑃 ≅ ̅̅̅̅ 𝐻𝑃 SSS: B.𝐻𝐸 ̅̅̅̅ ̅̅̅̅ ≅ 𝑃𝑂 ̅̅̅̅ ≅ 𝑃𝐻 D. 𝐻𝑃 ̅̅̅̅ Directions: Put identical markings on corresponding congruent parts to illustrate that the two triangles are congruent using the specified Congruence Postulate. 1. ∆GAB ≅ ∆PNG by SAS Congruence Postulate ̅̅̅̅ 𝐺𝐴 ≅ ̅̅̅̅ 𝑃𝑁 ∠A ≅ ∠N ̅̅̅̅ ≅ 𝑁𝐺 𝐴𝐵 ̅̅̅̅ 2. ∆CHA ≅ ∆GVN by SSS Congruence Postulate ̅̅̅̅ 𝐶𝐻 ≅ ̅̅̅̅ 𝐺𝑉 ̅̅̅̅ 𝐻𝐴 ≅ 𝑉𝑁̅̅̅̅ ̅̅̅̅ ≅ 𝐺𝑁 𝐶𝐴 ̅̅̅̅ 6  3. ∆PRN ≅ ∆ADM by ASA Congruence Postulate ∠P ≅ ∠A ∠R ≅ ∠D ∠N ≅ ∠M Can you illustrate the SAS, ASA, and SSS Congruence Postulate? How? ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ (Source: Emmanuel P. Abuzo et al., Mathematics 8: Learner’s Module, Pasig City: DepEd-IMCS, 2013, 353-357.) Let’s Sum It Up Activity 1 Directions: Complete each statement by filling in the blanks with the correct terms. Choose your answers from the box. included side two angles three angles three sides two sides included angle 1. _____________________ is the angle between two sides of the triangle. 2. _____________________is the side common to two angles of a triangle. 3. If _____________________ and an included side of one triangle are congruent to the corresponding two angles and an included side of another triangle, then the triangles are congruent. 4. If _____________________of a triangle are congruent to the three sides of another triangle, then the triangles are congruent. 5. If _____________________and an included angle of one triangle are congruent to the corresponding two sides and an included angle of another triangle, then the triangles are congruent. 7 Activity 2 Directions: Match the Triangle Congruence Postulates in Column A to their definitions in Column B. Write the letter of your answer on the space provided before each number. Column A Column B A. If two angles and an included side of one _____________1. SAS triangle are congruent to the corresponding two angles and an included side of another triangle, then the triangles are congruent. B. If three sides of a triangle are congruent to _____________2. ASA the three sides of another triangle, then the triangles are congruent. C. If two sides and an included angle of one triangle are congruent to the _____________3. SSS corresponding two sides and an included angle of another triangle, then the triangles are congruent. (Source: Emmanuel P. Abuzo et al., Mathematics 8: Learner’s Module, Pasig City: DepEd-IMCS, 2013, 353-357.) Let’s Assess Directions: Read each item carefully. Write the letter of the correct answer on the space provided before each number. _____1. Which is the correct congruence statements for the marked triangles? ̅̅̅ ≅ ̅̅̅̅ A. ̅𝐿𝑇 𝑀𝑆, ̅̅̅̅ 𝑀𝐸 , ̅̅̅̅ 𝐿𝑂 ≅ ̅̅̅̅̅ 𝑂𝑇 ≅ ̅̅̅̅ 𝐸𝑆, ∆LOT ≅ ∆MES ̅̅̅ ≅ ̅̅̅̅ B. ̅𝐿𝑇 𝑆𝑀, ̅̅̅̅ 𝑀𝐸 , ̅̅̅̅ 𝐿𝑂 ≅ ̅̅̅̅̅ 𝑂𝑇 ≅ ̅̅̅̅ 𝐸𝑆, ∆LOT ≅ ∆SME ̅̅̅ ≅ ̅̅̅̅ C. ̅𝐿𝑇 𝑀𝑆, ̅̅̅̅ 𝑀𝐸 , ̅̅̅̅ 𝑂𝐿 ≅ ̅̅̅̅̅ 𝑂𝑇 ≅ ̅̅̅̅ 𝑆𝐸, ∆LOT ≅ ∆MSE ̅̅̅̅, 𝐿𝑂 ̅̅̅̅ ≅ 𝑀𝑆 D. 𝑇𝐿 ̅̅̅̅ ≅ ̅̅̅̅̅ ̅̅̅̅ ≅ ̅̅̅̅̅ 𝑀𝐸 , 𝑂𝑇 𝑀𝐸 , ∆TOL ≅ ∆SME ______2. In ∆DOS, what side is included between ∠𝐷 and ∠𝑂? A. ̅̅̅̅ 𝐷𝑂 ̅̅̅̅ B. 𝐷𝑆 C. ̅̅̅̅ 𝑆𝐷 Figure 1 ̅̅̅̅ D. 𝑆𝑂 ______3. In ∆DOS at figure 1. What angle is included between ̅̅̅̅ 𝐷𝑆 and ̅̅̅̅ 𝑆𝑂? A. ∠𝐷 B. ∠𝑂 C. ∠𝑆 D. ∠𝑆𝐷𝑂 ______4. What Congruence Postulate is defined by the statement “If two sides and an included angle of one triangle are congruent to the corresponding two sides and an included angle of another triangle, then the triangles are congruent”? A. ASA B. SAS C. AAS D. SSS 8 ______5. Which of the following statements is true about SSS Congruence Postulate? A. If three sides of a triangle are congruent to the three angles of another triangle, then the triangles are congruent. B. If three sides of a triangle are congruent to the three sides of another triangle, then the triangles are congruent. C. If three angles of a triangle are congruent to the three sides of another triangle, then the triangles are congruent. D. If three angles of a triangle are congruent to the three angles of another triangle, then the triangles are congruent. ______6. Miguel knows that in ∆MIG and ∆JAN, 𝑀𝐼 = 𝐽𝐴, 𝐼𝐺 = 𝐴𝑁, 𝑎𝑛𝑑 𝑀𝐺 = 𝐽𝑁. Which postulate or theorem can he use to prove that the triangles are congruent? A. ASA B. SAS C. AAS D. SSS ______7. In the given figure, corresponding congruent parts are marked. What must be the additional corresponding parts to make the triangles congruent by ASA congruence postulate? A D A. ∠𝐵 ≅ ∠𝐸 B. ∠𝐶 ≅ ∠𝐹 C. ̅̅̅̅ 𝐴𝐵 ≅ ̅̅̅̅ 𝐷𝐸 ̅̅̅̅ D. 𝐶𝐵 ≅ ̅̅̅̅ 𝐹𝐸 C B F E ______8. Which postulate or theorem can be used to prove that the triangles in the figure on the right are congruent? A. ASA C. AAS B. SAS D. SSS ______9. Which of the following illustrates the ASA congruence postulate? A. C. B. D. ______10. Which postulate or theorem can be used to prove that the triangles in the figure on the right are congruent? A. ASA C. AAS B. SAS D. SSS (Source: Emmanuel P. Abuzo et al., Mathematics 8: Learner’s Module, Pasig City: DepEd-IMCS, 2013, 345-348.) 9  Answer Key Let’s Try 1. A 3. A 5. B 7. B 9. B 2. C 4. B 6. D 8. D 10. C Let’s Practice Let’s Do More Activity 1 Activity 2 Activity 1 1. 𝐵 2. 𝐶 1. SSS 1. FAT 3. 𝐴 2. ASA 2. JET 3. SAS 3. GVN Activity 2 4. SSS 4. PNG 5. ASA Let’s Sum it Up Activity 1 1. included angle 2. included side 3. two angles 4. three sides 5. two sides Activity 2 1. C 2. A 3. B Let’s Assess 1. A 3. C 5. B 7. B 9. C 2. A 4. B 6. D 8. B 10. D References 1. Book Bernabe, Julieta G., Cecile M. De Leon, and Soledad Jose-Dilao. Geometry: Textbook for Third Year. DepEd-IMCS, 2002. 2. Module Abuzo, Emmanuel P., Merden L. Bryant, Jem Boy B. Cabrella, Belen P. Caldez, Melvin M. Callanta, Anastacia Proserfina I. Castro, Alicia R. Halabaso, Sonia P. Javier, Roger T. Nocom, and Concepcion S. Ternida. Mathematics 8: Learners Module. Pasig City: Department of Education, 2013. 10 FEEDBACK SLIP A. FOR THE LEARNER Thank you very much for using this CLAS. This learner’s material is aimed at ensuring your worthwhile learning through the help of your family members. For feedback purposes, kindly answer YES NO the following questions: 1. Are you happy and contented with your learning experiences using this CLAS? 2. Were you able to follow the processes and procedures that were indicated in the different learning activities? 3. Were you guided by anybody from your family while using this CLAS? 4. Was there any part of this CLAS that you found difficult? If yes, please specify what it was and why. B. FOR THE PARENTS / GUARDIANS Do you have any suggestions or recommendations on how we can make improvements to this CLAS to better serve the learners? Yes (Please indicate what this is/these are.) None Contact Number: __________________________________ NAME OF SCHOOL: Teacher’s Name and Signature: Parent’s / Guardian’s Name and Signature: Date Received: Date Returned: 11