Transcript 4-6 Congruence in Right Triangles

Congruence in Right Triangles
LESSON 4-6
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.
Quick Check
HELP
GEOMETRY
Congruence in Right Triangles
LESSON 4-6
Additional Examples
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
Additional Examples
Quick Check
Write a two–column proof.
Given: ABC and DCB are right angles, AC
Prove: ABC
DCB
Statements
Reasons
1. ABC and  DCB are
right angles.
1. Given
2.
2. Definition of a right triangle
ABC and DCB are
right triangles.
3. AC DB
4. BC CB
5.
HELP
ABC
DB
DCB
3. Given
4. Reflexive Property of Congruence
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).
GEOMETRY