Honors GeometryIsosceles Triangles

LegLeg

BaseAngles

Base

Remember– the properties of an isosceles triangle…..

Vertex Angle

Vertex Angle

Investigating Isosceles TrianglesUse a straightedge to draw an

ACUTE ISOSCELES triangle-- where and is the acute vertex angle.

Use scissors to cut the triangle outThen fold the triangle as shownREPEAT the procedure for an

OBTUSE ISOSCELES triangle -- where and is the obtuse vertex angle.

PAB PA PBAPB

XYZXY XZ ZXY

What observation can you make about the base angles?

Isosceles Triangle TheoremIf two sides of a triangle are congruent,

then the angles opposite them are congruent.

Use ALGEBRA to find the missing measures(not drawn to scale)1.

44

x y

30

mr

Use ALGEBRA to find the missing measures(not drawn to scale)1.

44

x y

30

mr

x+y+ 44 = 180 Sumx = y because the two

base angles are congruent to each other b/c they are opposite congruent sides

180 = x + x + 44 136 = 2x68=x68 = y

68 68

Use ALGEBRA to find the missing measures(not drawn to scale)

2.

30°

mr

Find the missing measures(not drawn to scale)

30 + r + m = 180r is the other base

angle and must be 30° b/c its opposite from a congruent side.

30 + 30 + m = 18060 + m = 180m = 120

2.

30°

mr30°12

0°

Isosceles Triangle TheoremIf two sides of a triangle are congruent,

then the angles opposite them are congruent.

Given: Prove:

NC NYC Y

Proof of Base Angles TheoremGiven: Prove:

3. CH HY

4. NH NH

NC NY C Y Statements

1. Label H as the midpoint of CY

2. Draw NH

5. NC NY6. NHC NHY

7. C Y

Reasons

1. Ruler Postulate2. 2 points determine a

line

3. Def. of midpoint

4. Reflexive Prop

5. Given

6. SSS

7. CPCTC

Converse of the Isosceles Triangle TheoremIf two angles of a triangle are congruent,

then the sides opposite them are congruent.

A

R

T

Corollary--A corollary is a theorem that follows easily

from a theorem that has already been prove.

Corollary : If triangle is equilateral, then it is also equiangular. A

B C•Corollary : If a triangle is equiangular, then it is also equilateral. W

E R