4.6 The Isosceles 4.6 The Isosceles Triangle Triangle

TheoremsTheoremsBase Angles and Opposite Base Angles and Opposite

SidesSides

Hypotenuse - LegHypotenuse - Leg

Parts of an Isosceles Triangle

Vertex

legleg

base

anglebaseanglebase

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

A

B C

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Given:

Bisect angle A

So by SAS

So

By C.P.C.T.

A

B CD

ACAB

CADBAD

CADBAD

CB

Corollary of Isosceles Triangle Theorem

An equilateral triangle is also equiangular

An equilateral triangle has three 60 degree angles.

The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

Another Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

What is this compared to

the Isosceles Triangle Theorem?

An equiangular triangle is also equilateral.

Solve for x and y

50

xy

Solve for angles… 2,3,4

Given:

AB

C2

3 4

140

ACBC

Hypotenuse – Leg (HL)

In two right triangles if the hypotenuse and one leg are congruent, then the triangles are congruent.

To use this you must show Right Triangles

Solve for v

22 v

42 v

5v

Find the missing side

62

6256

4142

HomeworkHomework

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##9 – 25 odd, 9 – 25 odd,

34 -37, 3934 -37, 39

HomeworkHomework

Page 239 – 242 Page 239 – 242

##8 -24 even8 -24 even

29- 3329- 33