Isosceles Triangle ABC

• Vertex Angle• Leg

• Base

• Base Angles

A

B C

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Theorem 4.6-Base Angles Theorem

• If two sides of a triangle are congruent,

• Then, the angles opposite them are congruent.

A

B C

Prove Theorem 4.6

• Given:

• Prove:

A

B C

_____ _____

AB AC

B C

Theorem 4.6-Base Angles Theorem

• The converse:• If two sides of a

triangle are congruent,

• Then, the angles opposite them are congruent.

A

B C

Theorem 4.7-Converse of the Base Angles Theorem

• If two angles of a triangle are congruent,

• Then the sides opposite them are congruent.

A

B C

Prove Theorem 4.7

• Given:

• Prove:

A

B C

_____ _____

AB AC

B C

Now that you know about these theorems….test yourself with

some problems…

Solve for x and y

Solve for x and y

Solve for x and y

Corollary to theorem 4.6 & 4,7

• If a triangle is equilateral,

• Then it is equiangular

• If a triangle is equiangular

• Then it is equilateral.

B

A C

Theorem 4.8-Hypotenuse-Leg (HL) Congruence Theorem

• If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle,

• Then the two triangles are congruent.

by the HL theorem.

FDE ABC

F

D ECB

A

Solve for x

Solve for x

Solve for x

Write the equation of the line

• Passing through P(1,1) and

• Perpendicular to y = -3x - 4

Given the points (5,8) & (-12,1)

• What is the distance between them?

• What are the coordinates of the midpoint?

Assignment 4.6