4.6 - Congruence in Right Triangles.notebook

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

11/29: Warm Up

1.  Is DE = DF?  Explain.

2.   What is the value of x?

D

E

F61°

58°

(5x)° (3x + 28)°

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Day 7: Congruence in Right Triangles Date: 11/29

Right Triangle

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Theorem 4.6:Hypotenuse-Leg Congruence Theorem ( )

“If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles

are congruent.”

If Hypotenuse _________________, and

Leg _________________, and

then __________________________________

A

B C

X

Y Z

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Ex 1) Is it possible to show that ABC = ADC using the HL congruence theorem? Explain.

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Ex 2) Use the figure to write a two­column proof to prove that TUV = XWV.

Statements Reasons

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Ex 3) Use the figure to write a two­column proof to prove that ABC = ADC

Statements Reasons

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Ex 4) Does the diagram give enough information to prove that the triangles are congruent? If so, state the postulate or theorem you would use. If not, explain why.

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Ex 5) Use the diagram to write a two­column proof to prove that PQS = RQS

Statements Reasons

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Ex 6) Use the diagram to write a two­column proof to prove that TRS = WUV

Statements Reasons

4.6 ­ Congruence in Right Triangles.notebook

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November 29, 2016

Homework: pg. 277 #1 – 3, 5 – 10, 14

(proofs: #5, 6, 7, 8, 14)