Proving of Two Congruence Triangle (SSS, SAS, ASA, AAS).pptx

School purposes

1. Good Morning!

2. LESSON OBJECTIVES By the end of the lesson, the students can: Determine what additional information is needed to prove two triangles congruent; Show interest on the importance of proving two triangles are congruent using two-column proof; and Demonstrate on how you prove the two triangles are congruent in real-life situation.

3. CLASSROOM RULES L isten when the teacher is talking. E ngage by raising your hand to speak. A ct kindly and respectfully. D emonstrate good behavior.

4. ACTIVITY TIME! Work in groups and take turns. Flip two cards (one statement, one reason). If they match, keep them; if not, flip them back and wait for your turn. Remember the cards to find matches faster. The group with the most matches wins!

5. ACTIVITY TIME! What did you notice about the activity? Was it easy or hard to find the correct matches? Why? How did your group work together to solve the matches?

6. MATH 8 - FOURTH QUARTER PROVING CONGRUENCE OF TWO TRIANGLES USING TWO-COLUMN PROOF

7. STEP 1 . Identify what the given and what is to be proved. STEP 2 . Identify the congruence theorem to be used and the additional information needed and proof. STEP 3 . Write down the statements and the reasons in a two- column proof. Make sure the last statement contains what should be proved. STEPS IN PROVING CONGRUENCE OF TWO TRIANGLES

8. EXAMPLE #1: Prove that .   STEP 1 Given : Prove :   STEP 2 is the common side of ∆REC and ∆CAR, so by reflexive property. Hence, SSS postulate can be used to prove because each of the three sides of ∆REC is congruent respectively to the three sides of ∆CAR.  

9. EXAMPLE #1: Prove that △RAW ≅ △RSD. STEP 3 Two-column Proof: STATEMENTS REASONS 1. 1. Given 2. 2. Reflexive Property of Equality (RPE) 3. 3. SSS Congruence Postulate STATEMENTS REASONS 1. Given 2. Reflexive Property of Equality (RPE) 3. SSS Congruence Postulate

10. Corresponding Parts of Congruent Triangle are Congruent (CPCTC) If two triangles are congruent, then their corresponding angles and their corresponding sides are congruent.

11. EXAMPLE #2: Prove that .   Given : Prove :  

12. EXAMPLE #2: Prove that .   Given : Prove :   STATEMENTS REASONS 1. 1. Given 2. 2. Reflexive Property of Equality (RPE) 3. 3. SSS Congruence Postulate 4. 4. CPCTC STATEMENTS REASONS 1. Given 2. Reflexive Property of Equality (RPE) 3. SSS Congruence Postulate 4. CPCTC Two-column Proof:

13. TRY ME! Given : Prove :   Prove that .  

14. TRY ME! Given : Prove :   Prove that .   Two-column Proof: STATEMENTS REASONS 1. 1. Given 2.∠WRA and ∠DRS are vertical angles 2. Definition of vertical angle 3. 3. SAS Congruence Postulate 4. 4. CPCTC STATEMENTS REASONS 1. Given 2.∠WRA and ∠DRS are vertical angles 2. Definition of vertical angle 3. SAS Congruence Postulate 4. CPCTC

15. TRY ME! Given : bisects at Prove :   Prove that  

16. TRY ME! Given : bisects at Prove :   Prove that .   Two-column Proof: STATEMENTS REASONS 1. bisects at 1. Given 2. 2. Given 3. 3. Definition of Angle Bisector 4. 4. RPE 5. 5. AAS Cong. The. 6. 6. CPCTC STATEMENTS REASONS 1. Given 2. Given 3. Definition of Angle Bisector 4. RPE 5. AAS Cong. The. 6. CPCTC

17. EXAMPLE #3: Prove that .   Given : is a midpoint of Prove :  

18. EXAMPLE #3: Prove that .   STATEMENTS REASONS 1. 1. Given 2.∠ASV and ∠ESV are right angles 2. Definition of perpendicular lines 3. 3. Right Angle Theorem 4. is a midpoint of 4. Given STATEMENTS REASONS 1. Given 2.∠ASV and ∠ESV are right angles 2. Definition of perpendicular lines 3. Right Angle Theorem 4. Given Two-column Proof: Given : is a midpoint of Prove :  

19. EXAMPLE #3: Prove that .   STATEMENTS REASONS 5. 5. Definition of Midpoint 6. 6. Reflexive Property of Equality 7. 7. LL Congruence Theorem 8. 8. CPCTC STATEMENTS REASONS 5. Definition of Midpoint 6. Reflexive Property of Equality 7. LL Congruence Theorem 8. CPCTC Two-column Proof: Continuation Given : is a midpoint of Prove :  

20. The Isosceles Triangle Theorem (ITT) If two sides of a triangle are congruent, then the angles opposite them are also congruent.

21. EXAMPLE #3: Prove that .   Given : is a midpoint of Prove :  

22. EXAMPLE #3: Prove that .   STATEMENTS REASONS 1. 1. Given 2. ∆𝐷𝐴𝐿 is an isosceles triangle 2. Definition of Isosceles Triangle 3. 3. Isosceles Triangle Theorem 4. is a midpoint of 4. Given STATEMENTS REASONS 1. Given 2. ∆𝐷𝐴𝐿 is an isosceles triangle 2. Definition of Isosceles Triangle 3. Isosceles Triangle Theorem 4. Given Two-column Proof: Given : is a midpoint of Prove :  

23. EXAMPLE #3: Prove that .   STATEMENTS REASONS 5. 5. Definition of Midpoint 6. 6. SAS Congruence Postulate 7. ∠3 = ∠4 7. CPCTC STATEMENTS REASONS 5. Definition of Midpoint 6. SAS Congruence Postulate 7. ∠3 = ∠4 7. CPCTC Two-column Proof: Continuation Given : is a midpoint of Prove :  

24. The Converse of the Isosceles Triangle Theorem (Converse of ITT) If two angles of a triangle are congruent, then the sides opposite them are also congruent.

25. What Can I Do! INSTRUCTIONS : Work in teams to solve a triangle congruence case. Match each statement with the correct reason and reason with the correct statement. Arrange them in order to complete the proof.

26. What Can I Do! INSTRUCTIONS : 4. Stand still when finished and wait for the teacher to notice your group. 5. While standing, one person in your group will say: " We're Detective Group [Number], and we are ready to present our case, Ma'am ." 6. Then choose a presenter who will explain your proof. 7. Present your proof using the script below.

27. Thank You for LISTENING!