Triangle Congruencies

For each pair of triangles, tell:a) Are they congruentb) Write the triangle congruency statementc) Give the postulate that makes them

congruent.

For each pair of triangles, tell:a) Are they congruentb) Write the triangle congruency statementc) Give the postulate that makes them

congruent.

For each pair of triangles, tell:a) Are they congruentb) Write the triangle congruency statementc) Give the postulate that makes them

congruent.

For each pair of triangles, tell:a) Are they congruentb) Write the triangle congruency statementc) Give the postulate that makes them

congruent.

For each pair of triangles, tell:a) Are they congruentb) Write the triangle congruency statementc) Give the postulate that makes them

congruent.

For each pair of triangles, tell:a) Are they congruentb) Write the triangle congruency statementc) Give the postulate that makes them

congruent.

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

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

STATEMENTS REASONS1. AD‖BC 1. Given2. EAD and ECB are alternate interior angles. 2. Definition of Alternate Interior Angles3. EAD≅ECB 3. Alt. Int. s Theorem4. AED and BEC are vertical angles. 4. Definition of Vertical s5. AED≅BEC 5. Vertical s Theorem6. AD ≅ CB 6. Given7. ΔAED ≅ ΔCEB 7. AAS ≅You could also use EBC and EDA as alternate interior angles.

2.

STATEMENTS REASONS1.MJ ≅ ML 1. Given2. L ≅ J 2. Base Angles Thm3. JMK ≅ LMK 3. Given4. JM ≅ LM 4. Given5. ΔJKM ≅ ΔLKM 5. ASA ≅Another version on the next slide…

2.

STATEMENTS REASONS1. KM ⟘ JL 1. Given2.JKM and LKM are right angles. 2. ⟘ lines form right

s3. ΔJKM and ΔLKM are right Δs. 3. Def. of Right Δs4. JM ≅ LM (hypotenuse) 4. Given5. KM ≅ KM (leg) 5. Reflexive POC6. ΔJKM ≅ ΔLKM 5. HL ≅

Another version on the next slide…

2.

STATEMENTS REASONS1. KM ⟘ JL 1. Given2.JKM and LKM are right angles. 2. ⟘ lines form right

s3.JKM ≅ LKM 3. All right s are ≅.4.JMK ≅ LMK 4. Given5. JM ≅ LM 5. Given6. ΔJKM ≅ ΔLKM 6. AAS ≅

Another version on the next slide…

2.

STATEMENTS REASONS1. KM ≅ KM 1. Reflexive POC2. JM ≅ LM 2. Given3.JMK ≅ LMK 3. Given4. ΔJKM ≅ ΔLKM 4. 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 ≅.

STATEMENTS REASONS1. B is the midpoint of DC. 1. Given2. DB ≅ BC 2. Definition of Midpoint3. AB ≅ AB 3. Given4. AB ⟘ DC 4. Given5. ABD and ABC are right s.5. Definition of ⟘ lines.6. ABD ≅ ABC 6. All right s are congruent.7. ΔABD ≅ ΔABC 7. SAS ≅