Download 4-6 Congruence in Right Triangles Objective SWBAT prove right

4-6 Congruence in Right Triangles
Objective
SWBAT prove right triangles congruent using the Hypotenuse-Leg Theorem
Important Info
In a right triangle, the side ______________ the right angle is called the
_______________. It is the ____________ side in the triangle. The other
two sides are called the _______.
Theorem 4-6
Hypotenuse-Leg (HL) Theorem
If the ____________ and a ____ of one right triangle are congruent to the
_____________ and a _____ of another right triangle, then they are congruent.
Key Concept
Conditions for the HL Theorem
To use this theorem, the triangle must meet 3 conditions:
1. There are ____ right triangles.
2. The triangles have congruent _____________.
3. There is one pair of congruent _______.
Example 1
Using the HL Theorem
<ADC and <BDC are right angles and AC = BC. Are triangle ADC and triangle
BDC congruent? Explain, and include a picture.
Given: <PRS and <RPQ are right angles, SP = QR
Prove: Triangle PRS = triangle RPQ
S
Example 2
Writing a Proof Using the HL Theorem
Given: BE bisects AD at C, AB BC, DE EC, AB = DE
Prove: Triangle ABC = Triangle DEC
B
A
Given: CD = EA, AD is the perpendicular bisector or CE
Prove: Triangle CBD = triangle EBA
A
Homework
___________________________
P
Q
R
D
C
E
C
B
E
D