# 4.6 Isosceles Triangles - PowerPoint PPT Presentation

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4.6 Isosceles Triangles. Objectives. Use properties of isosceles triangles Use properties of equilateral triangles. Properties of Isosceles Triangles. The  formed by the ≅ sides is called the vertex angle . The two ≅ sides are called legs . The third side is called the base .

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4.6 Isosceles Triangles

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4.6 Isosceles Triangles

### Objectives

• Use properties of isosceles triangles

• Use properties of equilateral triangles

### Properties of Isosceles Triangles

• The  formed by the ≅ sides is called the vertex angle.

• The two ≅ sides are called legs. The third side is called the base.

• The two s formed by the base and the legs are called thebase angles.

vertex

leg

leg

base

### Isosceles Triangle Theorem

• Theorem 4.9If two sides of a ∆ are ≅, then the s opposite those sides are ≅ (if AC ≅ AB, then B ≅ C).

A

B

C

### The Converse of Isosceles Triangle Theorem

• Theorem 4.10

If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).

Name two congruent angles (not indicated).

### Example 2:

Name two congruent segments (not indicated).

By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So,

### Example 2:

a. Name two congruent angles.

b. Name two congruent segments.

### Properties of Equilateral ∆s

• Corollary 4.3A ∆ is equilateral if it is equiangular.

• Corollary 4.4Each  of an equilateral ∆measures 60°.

EFG is equilateral, and bisects bisectsFindand

Each angle of an equilateral triangle measures 60°.

Since the angle was bisected,

### Example 3a:

is an exterior angle of EGJ.

### Example 3a:

Exterior Angle Theorem

Substitution

EFG is equilateral, and bisects bisectsFind

### Example 3b:

Linear pairs are supplementary.

Substitution

Subtract 75 from each side.

ABC is an equilateral triangle. bisects

a. Find x.