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Math 8 Quarter 3 Topic: CONGRUENT TRIANGLES
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- 10. Among the givenfigures, which pair of triangles is congruent?
- 11. In figure 1,although Δ𝐻𝐼𝐺 and Δ 𝐾𝐿𝑀 have the same shape, they are not congruent because they differ in size.
- 12. The Δ𝐷𝐸𝐹 andΔ𝑁𝑂𝑃 in figure 2, have the same area but they have different angles so they cannot be considered as congruent triangles.
- 13. Two figures arecongruent if they have the same shape and size. Can we consider figure 3 as congruent triangles?
- 14. In figure 3,if triangles Δ𝐴𝐵𝐶 and Δ𝑇𝑆𝑅 can match up their vertices by flipping and rotating the figures until they overlap exactly then you will notice that the corresponding sides and the corresponding angles that overlapped are congruent.
- 15. Notice the orderof letters is according to the CORRESPONDING VERTICES 𝐴 ↔ 𝑇 𝐵 ↔ 𝑆 𝐶 ↔ 𝑅 𝐴𝐵𝐶 ↔ 𝑇𝑆𝑅 CORRESPONDING SIDES 𝐴𝐵̅̅̅̅̅̅̅̅̅ ↔ 𝑇𝑆̅̅̅̅̅̅̅̅̅̅̅̅ 𝐵𝐶̅̅̅̅̅̅̅̅̅̅̅̅ ↔ 𝑆𝑅̅̅̅̅̅̅̅̅̅̅̅̅ 𝐴𝐶̅̅̅̅̅̅̅̅̅̅̅̅ ↔ 𝑇𝑅̅̅̅̅̅̅̅̅̅̅̅̅ CORRESPONDING ANGLES ∠𝐴 ↔ ∠𝑇 ∠𝐵 ↔ ∠𝑆 ∠𝐶 ↔ ∠R
- 16. CONGRUENT SIDES 𝐴 𝐵̅̅̅̅̅̅̅̅̅̅̅̅≅ 𝑇𝑆̅̅̅̅̅̅̅̅̅̅̅̅ 𝐵𝐶̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑆𝑅̅̅̅̅̅̅̅̅̅̅̅̅ 𝐴𝐶̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑇𝑅̅̅̅̅̅̅̅̅̅̅̅̅ CONGRUENT ANGLES ∠𝐴 ≅ ∠𝑇 ∠𝐵 ≅ ∠𝑆 ∠𝐶 ≅ ∠𝑅 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, Δ𝑨𝑩𝑪 ≅ Δ𝑻𝑺𝑹 Note that the identical markings indicate congruent parts
- 17. Example1 Given Δ𝑷𝑹𝑶 ≅Δ𝒀𝑿𝒁.Identify the congruent sides and congruent angles. Solution: Corresponding Angles ∠𝑃 ≅ ∠𝑌 or ∠𝑅𝑃𝑂≅ ∠𝑋𝑌𝑍 ∠𝑅 ≅ ∠𝑋 or ∠𝑃𝑅𝑂≅ ∠𝑌𝑋𝑍 ∠𝑂 ≅ ∠𝑍 or ∠𝑃𝑂𝑅≅ ∠𝑌𝑍𝑋 Corresponding Sides 𝑃𝑂̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑌𝑍̅̅̅̅̅̅̅̅̅̅̅̅ or 𝑂𝑃̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑍𝑌̅̅̅̅̅̅̅̅̅̅̅̅ 𝑃𝑅̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑌𝑋̅̅̅̅̅̅̅̅̅̅̅̅ or 𝑅𝑃̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑋𝑌̅̅̅̅̅̅̅̅̅̅̅̅ 𝑅𝑂̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑋𝑍̅̅̅̅̅̅̅̅̅̅̅̅ or 𝑂𝑅̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑍𝑋̅̅̅̅̅̅̅̅̅̅̅̅
- 18. Example2 List the6 pairs of corresponding congruent parts of the given triangles and name the two congruent triangles. Solution: Recall the identical markings indicate congruent parts. Corresponding Angles ∠𝐿 ≅∠𝑃 ∠𝑈 ≅∠𝑆 ∠𝑉 ≅∠𝑇 Corresponding Sides 𝐿𝑉̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑃𝑇̅̅̅̅̅̅̅̅̅̅̅̅ 𝑉𝑈̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑇𝑆̅̅̅̅̅̅̅̅̅̅̅̅ 𝐿𝑈̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑃𝑆̅̅̅̅̅̅̅̅̅̅̅̅ Thus, Δ𝐿𝑈𝑉 ≅ Δ𝑃𝑆𝑇
- 19. Example3 Show thattwo triangles are congruent. Solution: Recall the identical markings indicate congruent parts. Corresponding Angles ∠𝐴 ≅∠𝑉 ∠𝑇 ≅∠𝑈 ∠𝑀 ≅∠𝐿 Corresponding Sides 𝑉𝑈̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝐴𝑇̅̅̅̅̅̅̅̅̅̅̅̅ 𝐿𝑈̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑀𝑇̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 𝐿𝑉̅̅̅̅̅̅̅̅̅̅̅̅ ≅ 𝑀𝐴̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ Thus, Δ𝑉UL ≅ ΔATM
- 20. ACTIVITY 1 LET’SPRACTICE! Directions: Show that the legs of the swing are congruent triangles. Complete the list of corresponding congruent parts and name the congruent triangles. Corresponding Angles 1. _______________ 2. _______________ 3. _______________ Corresponding Sides 4. _________ ______ 5. _______________ 6. _______________ 7. Therefore, Δ________ ≅ Δ_______ ∠S ≅ ∠F ∠K ≅ ∠N ∠Y ≅ ∠U SK̅̅̅̅̅̅̅̅̅̅̅̅ ≅ FN̅̅̅̅̅̅̅̅̅̅̅̅ K̅̅̅̅̅̅̅̅̅̅̅̅Y ≅ NU̅̅̅̅̅̅̅̅̅̅̅̅ SY̅̅̅̅̅̅̅̅̅̅̅̅ ≅ FU̅̅̅̅̅̅̅̅̅̅̅̅ SKY FNU
- 21. ACTIVITY 2 KEEPPRACTICING! Direction: Answer the following. A. If Δ𝑀𝐴𝑇 ≅ Δ𝐺𝐸𝑂, determine the corresponding congruent sides and angles of the following: 1. ∠𝐴 ________ 2. 𝐸𝑂̅̅̅̅̅̅̅̅̅̅̅̅ ________ 3. ∠𝐺 ________ 4. ∠𝑂 ________ 5. 𝑇𝑀̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ________ ∠A ≅ ∠E EO̅̅̅̅̅̅̅̅̅̅̅̅ ≅ AT̅̅̅̅̅̅̅̅̅̅̅̅ ∠G ≅ ∠M ∠O ≅ ∠T TM̅̅̅̅̅̅̅̅̅̅̅̅ ≅ OG̅̅̅̅̅̅̅̅̅̅̅̅
- 22. ACTIVITY 2 TESTYOURSELF! Direction: Tell whether the following pair of sides or angles is corresponding sides, corresponding angles or neither. 1. 𝑁𝑀̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ and 𝐷𝑌̅̅̅̅̅̅̅̅̅̅̅̅ 2. ∠𝑀 𝑎𝑛𝑑 ∠𝐷 3. ∠𝑂 𝑎𝑛𝑑 ∠𝐴 4. 𝑂𝑀̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ and 𝐴𝑌̅̅̅̅̅̅̅̅̅̅̅̅ 5. 𝑁𝑂̅̅̅̅̅̅̅̅̅̅̅̅ and 𝐷𝑌̅̅̅̅̅̅̅̅̅̅̅̅ Corresponding sides neither Corresponding angles Corresponding sides neither
- 23. ➢ Two figuresare congruent if they have the same shape and size. ➢ Two triangles are congruent if there exist a one-to-one correspondence between their vertices such that their corresponding sides are congruent and all their corresponding angles are congruent ➢ Two triangles are congruent if and only if their corresponding parts are congruent. WRAP-UP Remember that…
- 41. 35° 16cm 8cm 105° m∠ZEY = 180– (35+40) m∠ZEY = 180 – 75
- 42. 35° 16cm 8cm 105° m∠ZEY = 180– (35+40) m∠ZEY = 180 – 75 RS+ SX+RX =12 + 16 + 8 36 cm
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- 70. 1. Which ofthe following does NOT illustrate congruent figures? A. Hour Glass C. Pawns in a chessboard B. Roofs of Houses D. Truss Bridges POSTTEST Directions. Identify what is being asked in each question. Write the letter of the correct answer on a separate paper. 2. If Δ𝑀𝐴𝑋 ≅ Δ𝐾𝐹𝐶, which angle is congruent to∠𝑋? A. ∠𝐶 B. ∠𝐹 C. ∠𝐾 D. ∠𝑀 3. If ΔDOH ≅ ΔRAE, which side is congruent to side 𝐷𝐻̅̅̅̅̅̅̅̅̅̅̅̅? A. 𝐴𝐸̅̅̅̅̅̅̅̅̅̅̅̅ B. 𝐴𝑅̅̅̅̅̅̅̅̅̅̅̅̅ C. 𝐸𝑅̅̅̅̅̅̅̅̅̅̅̅̅ D. 𝑅𝐸̅̅̅̅̅̅̅̅̅
- 71. POSTTEST For item numbers4-5, refer to the figure at the right. 4. In the figure, which angle corresponds to ∠𝐴 ? A.∠B C. ∠𝑇 A.∠𝑋 D. ∠𝑍 5. In the figure, which segment corresponds to 𝑇𝑋̅̅̅̅̅̅̅̅̅̅̅̅ ? A. 𝐴𝐵̅̅̅̅̅̅̅̅̅̅̅̅ C. 𝐴𝐶̅̅̅̅̅̅̅̅̅̅̅̅ B. 𝐵𝐴̅̅̅̅̅̅̅̅̅̅̅̅ D. 𝐶𝐵̅̅̅̅̅̅̅̅̅
- 72. 1. Which ofthe following does NOT illustrate congruent figures? A. Hour Glass C. Pawns in a chessboard B. Roofs of Houses D. Truss Bridges POSTTEST Directions. Identify what is being asked in each question. Write the letter of the correct answer on a separate paper. 2. If Δ𝑀𝐴𝑋 ≅ Δ𝐾𝐹𝐶, which angle is congruent to∠𝑋? A. ∠𝐶 B. ∠𝐹 C. ∠𝐾 D. ∠𝑀 3. If ΔDOH ≅ ΔRAE, which side is congruent to side 𝐷𝐻̅̅̅̅̅̅̅̅̅̅̅̅? A. 𝐴𝐸̅̅̅̅̅̅̅̅̅̅̅̅ B. 𝐴𝑅̅̅̅̅̅̅̅̅̅̅̅̅ C. 𝐸𝑅̅̅̅̅̅̅̅̅̅̅̅̅ D. 𝑅𝐸̅̅̅̅̅̅̅̅̅
- 73. POSTTEST For item numbers4-5, refer to the figure at the right. 4. In the figure, which angle corresponds to ∠𝐴 ? A.∠B C. ∠𝑇 B. ∠𝑋 D. ∠𝑍 5. In the figure, which segment corresponds to 𝑇𝑋̅̅̅̅̅̅̅̅̅̅̅̅ ? A. 𝐴𝐵̅̅̅̅̅̅̅̅̅̅̅̅ C. 𝐴𝐶̅̅̅̅̅̅̅̅̅̅̅̅ B. 𝐵𝐴̅̅̅̅̅̅̅̅̅̅̅̅ D. 𝐶𝐵̅̅̅̅̅̅̅̅̅
- 79. Directions: Identify whatis being asked in each question. Write the letter of the correct answer.
- 84. POSTTEST Directions. Identify whatis being asked in each question. Write the letter of the correct answer on a separate paper.
- 85. POSTTEST Directions. Identify whatis being asked in each question. Write the letter of the correct answer on a separate paper.
- 86. POSTTEST Directions. Identify whatis being asked in each question. Write the letter of the correct answer on a separate paper.
- 87. 1. D 3. D 5.C 2. B 4. A ANSWER KEY:
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- 105. Reflexive Property of Congruence RightAngle Postulate PAIC Theorem PAIC Theorem Definition of Congruent Triangles
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- 107. Right Angle Postulate FA̅̅̅̅̅̅̅̅̅̅̅̅≅ CA̅̅̅̅̅̅̅̅̅̅̅̅ Reflexive Property of Congruence Definition of Angle Bisector ΔF𝑨T ≅ ΔCA𝑻