Chapter 4: Congruent Triangles

4.6

Congruence in Right Triangles

Right Triangles

leg

leg

hypotenuse

a2+b2=c2

Theorem 4-6

• Hypotenuse-Leg (HL) Theorem– 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.

Proof of the HL Theorem• Given: ΔPQR & ΔXYZ are right triangles

• Prove:

XYPQXZPR ,XYZPQR

P

Q RZY

X

Example 2• Given: AD is the perpendicular bisector of CE

• Prove:

EACD EBACBD

B

C

DA

E

Example 3• Given: W & K are right angles

• Prove:

KZWJ ZKJJWZ

W

J K

Z

Example 3a• Given: PRS & RPQ are right angles

• Prove:

QRSP RPQPRS

S R

P

Q

Example 4• Given: LO bisects angle MLN

• Prove:

LNONLMOM ,LNOLMO

L N

O

M

Homework

• p. 237

• 3, 4, 6-8, 10, 11, 13, 14