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4.6 Congruence in Right Triangles. Chapter 4 Congruent Triangles. 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*. Pythagorean Theorem. a 2 + b 2 = c 2. c.

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4 6 congruence in right triangles

4.6 Congruence in Right Triangles

Chapter 4

Congruent Triangles

4 6 congruence in right triangles2
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*

pythagorean theorem
Pythagorean Theorem

a2 + b2 = c2

c

*c is always the hypotenuse

a

b

pythagorean theorem4
Pythagorean Theorem

a2 + b2 = c2

c

*c is always the hypotenuse

3

4

pythagorean theorem5
Pythagorean Theorem

a2 + b2 = c2

13

*c is always the hypotenuse

a

5

pythagorean theorem6
Pythagorean Theorem

25

25

7

7

Are these triangles congruent?

congruence in right triangles
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.

congruence in right triangles8
Congruence in Right Triangles

Are the two triangles congruent?

A

X

B

C

Y

Z

proving triangles congruent
Proving Triangles Congruent

Given: WJ = KZ, <W and <K are right angles

Prove:ΔJWZ = ΔZKJ

Z

W

J

K

proving triangles congruent10
Proving Triangles Congruent

Given: CD = EA, AD is the perpendicular bisector of CE

Prove: ΔCBD = ΔEBA

C

D

A

B

E

practice
Practice
  • Pg 219 1-4 Write a two-column proof
  • Pg 219 5-8 Answer Question
  • Pg 220 9 - 10 Answer Question
  • Pg 220 11-12 Write a two-column proof
  • Pg 220-221 14-17
  • Pg 222 28 – 29 Write a two-column proof