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# CPCTC-lesson-17.1.pptx

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2.7.5 CPCTC
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# CPCTC-lesson-17.1.pptx

corresponding parts of congruent triangles are congruent

corresponding parts of congruent triangles are congruent

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### CPCTC-lesson-17.1.pptx

1. 1. CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT
2. 2. OBJECTIVE
3. 3. 1. Solve corresponding parts of congruent triangles; and 2. Prove that two triangles are congruent
4. 4. I AM EQUAL TO YOU
5. 5. Given the ∆𝐴𝐵𝐶 is congruent to ∆𝑃𝑄𝐶, complete the following statements. B A C Q P
6. 6. I. 𝑨𝑩 = 𝑷𝑸 = ________𝒄𝒎 B A C Q P
7. 7. B A C Q P 6cm II. 𝐁𝐂 = ________ = ________𝒄𝒎
8. 8. B A C Q P 5cm III. 𝐂𝐏 = ________ = ________𝒄𝒎
9. 9. B A C Q P 𝟑𝟎° 𝟏𝟐𝟎° 𝟑𝟎° IV. ∠𝑪𝑩𝑨 = ________ = ________°
10. 10. Know me more!
11. 11. CPCTC(Corresponding parts of Congruent triangles are congruent) Corresponding parts of congruent triangles, when two triangles are proved to be congruent, then each part of one triangle – three sides and three angles, is congruent to the corresponding parts of the other triangle
12. 12. Given: 𝐵𝐶 ≅ 𝐴𝐷, 𝐵𝐶 ∥ 𝐴𝐷 Prove: ∠𝐵 ≅ ∠𝐷 Example 1 A B C D
13. 13. Given: 𝐵𝐶 ≅ 𝐴𝐷, 𝐵𝐶 ∥ 𝐴𝐷 Prove: ∠𝐵 ≅ ∠𝐷 A B C D Statements Reasons 1. 𝐁𝐂 ≅ 𝐀𝐃, 𝐁𝐂 ∥ 𝐀𝐃 1. Given 2. ∠𝐁𝐂𝐀 ≅ ∠𝐃𝐀𝐂 2. Parallel – Alternative Interior Angle Postulate 3. 𝐀𝐂 ≅ 𝐀𝐂 3. Reflexive Property of Congruence 4. ∆𝐁𝐂𝐀 ≅ ∆𝐃𝐀𝐂 4. SAS Postulate 5. : ∠𝐁 ≅ ∠𝐃 5. CPCTC
14. 14. Given: ∠𝐵𝐴𝐷 ≅ ∠𝐶𝐴𝐷,∠𝐵𝐷𝐴 ≅ ∠𝐶𝐷𝐴 Prove: 𝐴𝐵 ≅ 𝐴𝐶 Example 2 A B D C
15. 15. A B D C Given: ∠𝐵𝐴𝐷 ≅ ∠𝐶𝐴𝐷,∠𝐵𝐷𝐴 ≅ ∠𝐶𝐷𝐴 Prove: 𝐴𝐵 ≅ 𝐴𝐶 𝑺𝒕𝒂𝒕𝒆𝒎𝒆𝒏𝒕𝒔 𝑹𝒆𝒂𝒔𝒐𝒏𝒔 1. ∠𝑩𝑨𝑫 ≅ ∠𝑪𝑨𝑫 ∠𝑩𝑫𝑨 ≅ ∠𝑪𝑫𝑨 Given 2. 𝑨𝑫 ≅ 𝑨𝑫 Reflexive Property of Congruence 3. ∆𝑩𝑨𝑫 ≅ ∆𝑪𝑨𝑫 ASA Postulate 4. 𝑨𝑩 ≅ 𝑨𝑪 CPCTC