chapter 4: congruent triangles
DESCRIPTION
Chapter 4: Congruent Triangles. 4.6 Congruence in Right Triangles. Right Triangles. 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. - PowerPoint PPT PresentationTRANSCRIPT
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