4.6 Congruence in Right Triangles

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4.6 Congruence in Right Triangles

• Chapter 4
• Congruent Triangles

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4.6 Congruence in Right Triangles
Right Triangle
Hypotenuse
Leg
Leg
The Hypotenuse is the longest side and is always
across from the right angle
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Pythagorean Theorem
a2 b2 c2
c
c is always the hypotenuse
a
b
4
Pythagorean Theorem
a2 b2 c2
32 42 c2
c
c is always the hypotenuse
9 16 c2
3
25 c2
c 5
4
5
Pythagorean Theorem
a2 b2 c2
a2 52 132
13
c is always the hypotenuse
a2 25 169
a
a2 144
a 12
5
6
Pythagorean Theorem
25
25
7
7
Are these triangles congruent?
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Congruence in Right Triangles

• Theorem 4-6 Hypotenuse-Leg (H-L) 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.

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Congruence in Right Triangles

• Are the two triangles congruent?

A
X
B
C
Y
Z
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Proving Triangles Congruent

• Given WJ KZ, ltW and ltK are right angles
• Prove ?JWZ ?ZKJ

Z
W
J
K
WJ KZ, ltW and ltK are right angles
Given
ltW ltK
All right angles are Congruent
JZ JZ
Reflexive Property
?JWZ ?ZKJ
H-L Theorem
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Proving Triangles Congruent

• Given CD EA, AD is the perpendicular bisector
  of CE
• Prove ?CBD ?EBA

C
D
A
B
CD EA, AD is the perpendicular bisector of CE
Given
E
Definition of bisector
CB EB
?CBD ?EBA
H-L Theorem
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Practice

• pg 219 1-8
• pg 221 16, 17, 19, 20
• Workbook 4.6