# 4-6_Congruence_in_Right_Triangles

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```					Congruence in Right Triangles
LESSON 4-6

One student wrote “ CPA        MPA by SAS” for the diagram
below. Is the student correct? Explain.

The diagram shows the following congruent parts.
CA   MA
CPA      MPA
PA   PA
There are two pairs of congruent sides and one pair of
congruent angles, but the congruent angles are not
included between the corresponding congruent sides.

The triangles are not congruent by the SAS Postulate,
but they are congruent by the HL Theorem.
Quick Check

HELP                                                                GEOMETRY
Congruence in Right Triangles
LESSON 4-6

XYZ is isosceles. From vertex X, a perpendicular is drawn
to YZ, intersecting YZ at point M. Explain why XMY         XMZ.

Quick Check

HELP                                                               GEOMETRY
Congruence in Right Triangles
LESSON 4-6

Quick Check

Write a two–column proof.
Given: ABC and DCB are right angles, AC         DB
Prove: ABC       DCB

Statements                          Reasons
1. ABC and  DCB are            1. Given
right angles.
2.    ABC and DCB are            2. Definition of a right triangle
right triangles.
3. AC DB                         3. Given
4. BC CB                         4. Reflexive Property of Congruence
5.     ABC       DCB             5. If the hypotenuse and a leg of one right
triangle are congruent to the hypotenuse
and a leg of another right triangle, then the
triangles are congruent. (HL Theorem).

HELP                                                                    GEOMETRY

```
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