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Congruence in Right Triangles
Lesson 4-6
Geometry
Additional Examples
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
PA
MPA
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.
Congruence in Right Triangles
Lesson 4-6
Additional Examples
Geometry
XYZ is isosceles. From vertex X, a perpendicular is drawn
to YZ, intersecting YZ at point M. Explain why XMY
XMZ.
Congruence in Right Triangles
Lesson 4-6
Geometry
Additional Examples
Write a two–column proof.
Given: ABC and DCB are right angles, AC
Prove: ABC
DCB
Statements
DB
Reasons
1. ABC and  DCB are
right angles.
2. ABC and DCB are
right triangles.
3. AC DB
4. BC CB
1. Given
5.
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).
ABC
DCB
2. Definition of a right triangle
3. Given
4. Reflexive Property of Congruence