Triangle Congruencies. For each pair of triangles, tell: a) Are they congruent b) Write the triangle congruency statement c) Give the postulate that makes.

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Presentation transcript:

Triangle Congruencies

For each pair of triangles, tell: a) Are they congruent b) Write the triangle congruency statement c) Give the postulate that makes them congruent.

Using the given postulate, tell which parts of the pair of triangles should be shown congruent.

Algebraic Problems 1

Algebraic Problems 2

Algebraic Problems 3

Algebraic Problems 4

Algebraic Problems 5 Solve for x in the isosceles triangle.

ON A PIECE OF PAPER TO BE HANDED IN, write the proof, including the Given, the Prove, the diagram and your tw0- column proof. You may use your notes. These will be graded on accuracy.

1. STATEMENTSREASONS 1. AD ‖ BC1. Given 2.  EAD and  ECB are alternate interior angles.2. Definition of Alternate Interior Angles 3.  EAD ≅  ECB 3. Alt. Int.  s Theorem 4.  AED and  BEC are vertical angles. 4. Definition of Vertical  s 5.  AED ≅  BEC 5. Vertical  s Theorem 6. AD ≅ CB 6. Given 7. ΔAED ≅ ΔCEB7. AAS ≅ You could also use  EBC and  EDA as alternate interior angles.

2. STATEMENTSREASONS 1.MJ ≅ ML1. Given 2.  L ≅  J2. Base Angles Thm 3.  JMK ≅  LMK3. Given 4. JM ≅ LM4. Given 5. ΔJKM ≅ ΔLKM5. ASA ≅ Another version on the next slide…

2. STATEMENTSREASONS 1.KM ⟘ JL1. Given 2.  JKM and  LKM are right angles.2. ⟘ lines form right  s 3.ΔJKM and ΔLKM are right Δs.3. Def. of Right Δs 4.JM ≅ LM(hypotenuse)4. Given 5.KM ≅ KM (leg)5. Reflexive POC 6. ΔJKM ≅ ΔLKM5. HL ≅ Another version on the next slide…

2. STATEMENTSREASONS 1.KM ⟘ JL1. Given 2.  JKM and  LKM are right angles.2. ⟘ lines form right  s 3.  JKM ≅  LKM 3. All right  s are ≅. 4.  JMK ≅  LMK4. Given 5.JM ≅ LM5. Given 6.ΔJKM ≅ ΔLKM6. AAS ≅ Another version on the next slide…

2. STATEMENTSREASONS 1.KM ≅ KM1. Reflexive POC 2.JM ≅ LM 2. Given 3.  JMK ≅  LMK3. Given 4. ΔJKM ≅ ΔLKM4. SAS ≅ If you can think of another way, let me know!

3. You don’t know the hypotenuses are congruent, so you can’t use HL ≅. STATEMENTSREASONS 1. B is the midpoint of DC.1. Given 2. DB ≅ BC 2. Definition of Midpoint 3.AB ≅ AB3. Given 4.AB ⟘ DC4. Given 5.  ABD and  ABC are right  s. 5. Definition of ⟘ lines. 6.  ABD ≅  ABC6. All right  s are congruent. 7.ΔABD ≅ ΔABC7. SAS ≅