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Lesson 7.pptx
- 1. slidesmania.com GRADE 8 STE-2 students!
- 2. slidesmania.com QUARTER 3: WEEK 7 Proving Statements on Triangle Congruence
- 3. slidesmania.com LEARNINGCOMPETENCY At the end of the lesson, you are able to: - prove statements on triangle congruence. (M8GE-IIIh-1)
- 5. slidesmania.com LET’S OBSERVE 6 Congruent Parts: CPCTC Corresponding Parts of Congruent Triangles are Congruent
- 6. slidesmania.com LET’S DISCUSS EXAMPLE # 1 ∆CAR ∆NEW
- 7. slidesmania.com EXAMPLE # 1 ∆CAR ∆NEW STATEMENTS REASONS 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 𝐶𝑅 ≅ 𝑁𝑊 ∠𝐶 ≅ ∠𝑁 𝐶𝐴 ≅ 𝑁𝐸 ∆𝐶𝐴𝑅 ≅ ∆𝑁𝐸𝑊 ∠𝐴 ≅ ∠𝐸 Given Given Given SAS Congruence Postulate CPCTC
- 8. slidesmania.com LET’S DISCUSS EXAMPLE # 2 Given: C is the midpoint of 𝐼𝐸 and 𝐴𝑆 Prove: 𝐼𝐴 ≅ 𝐸𝑆
- 9. slidesmania.com EXAMPLE # 2 Given: C is the midpoint of 𝐼𝐸 and 𝐴𝑆 Prove: 𝐼𝐴 ≅ 𝐸𝑆 STATEMENTS REASONS 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. C is the midpoint of 𝐼𝐸 and 𝐴𝑆 𝐼𝐶 ≅ 𝐸𝐶 𝐴𝐶 ≅ 𝑆𝐶 ∠𝐼𝐶𝐴 ≅ ∠𝐸𝐶𝑆 ∆𝐼𝐶𝐴 ≅ ∆𝐸𝐶𝑆 𝐼𝐴 ≅ 𝐸𝑆 Given Definition of a Midpoint Definition of a Midpoint Vertical angles are congruent or VAT- Vertical Angle Theorem SAS Congruence Postulate CPCTC
- 10. slidesmania.com LET’S DISCUSS EXAMPLE # 3 Given: 𝐼𝑃 ≅ 𝐴𝐷 ∠𝐼𝑃𝐷 ≅ ∠𝐴𝐷𝑃 Prove: ∠𝐼 ≅ ∠𝐴
- 11. slidesmania.com EXAMPLE # 3 Given: 𝐼𝑃 ≅ 𝐴𝐷 ∠𝐼𝑃𝐷 ≅ ∠𝐴𝐷𝑃 Prove: ∠𝐼 ≅ ∠𝐴 STATEMENTS REASONS 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 𝐼𝑃 ≅ 𝐴𝐷 ∠𝐼𝑃𝐷 ≅ ∠𝐴𝐷𝑃 𝐷𝑃 ≅ 𝑃𝐷 ∆𝐷𝐼𝑃 ≅ ∆𝑃𝐴𝐷 ∠𝑰 ≅ ∠𝑨 Given Given Reflexive Property SAS Congruence Postulate CPCTC
- 13. slidesmania.com LET’S CREATE A REAL-LIFE CONNECTION Two cars of the same model have hood braces that are identical, connect to the body of the car in the same place, and fit into the same slot in the hood.
- 14. slidesmania.com LET’S CREATE A REAL-LIFE CONNECTION Given: 𝐶𝐴 ≅ 𝑉𝐸 𝐴𝑅 ≅ 𝐸𝐻 𝑅𝐶 ≅ 𝐻𝑉 Complete the proof that the hood braces hold the hoods open at the same angle. Prove: ∠𝐴𝑅𝐶 ≅ ∠𝐸𝐻𝑉
- 15. slidesmania.com Given: 𝐶𝐴 ≅ 𝑉𝐸 𝐴𝑅 ≅ 𝐸𝐻 𝑅𝐶 ≅ 𝐻𝑉 Prove: ∠𝐴𝑅𝐶 ≅ ∠𝐸𝐻𝑉 STATEMENTS REASONS 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 𝑪𝑨 ≅ 𝑽𝑬 𝑨𝑹 ≅ 𝑬𝑯 𝑹𝑪 ≅ 𝑯𝑽 ∆𝐴𝑅𝐶 ≅ ∆𝐸𝐻𝑉 ∠𝐴𝑅𝐶 ≅ ∠𝐸𝐻𝑉 Given Given Given SSS Congruence Postulate CPCTC
- 16. slidesmania.com LET’S GENERALIZE How do you prove statements on triangle congruence?
- 17. slidesmania.com LET’S GENERALIZE To prove statements on _____________________ congruence, we can use the following; a) __________________ information b) Definition c) Triangle Congruence __________________________ d) Properties of __________________________________ e) CPCTC which stands for _________________ Parts of ____________________ Triangles are Congruent. triangle Given Postulates Equality/ Congruence Corresponding Congruent
- 18. slidesmania.com LET’S ASSESS WHAT YOU’VE LEARNED https://forms.gle/WTeoJ6jMKuwRRHt2A
- 20. slidesmania.com