Isosceles triangles
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Isosceles Triangles. Sec: 4.6 Sol: G.5. 3. Leg. Leg. 1. 2. Base. Properties of Isosceles Triangles. An isosceles triangle is a triangle with two congruent sides. The congruent sides are called legs and the third side is called the base. Vertex. Base Angles. A. B. C.

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Isosceles Triangles

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Isosceles triangles

Isosceles Triangles

Sec: 4.6

Sol: G.5


Properties of isosceles triangles

3

Leg

Leg

1

2

Base

Properties of Isosceles Triangles

An isosceles triangle is a triangle with two congruent sides.

The congruent sides are called legs and the third side is called the base.

Vertex

Base Angles


Theorem 4 9 isosceles triangle theorem

A

B

C

Theorem 4.9 Isosceles Triangle Theorem

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


Given prove

Given:Prove:


Find the measure of the missing angle

Find the measure of the missing angle

If

What is the measure of


Theorem 4 10

A

B

C

A

3x - 7

x+15

°

°

B

50

50

C

Theorem 4.10

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

Example:

Find the value of x.

Since two angles are congruent, the

sides opposite these angles must be

congruent.

3x – 7 = x + 15

2x = 22

X = 11

Lesson 3-2: Isosceles Triangle


Example

Example:

  • Name Two Congruent Angles:

  • Name Two Congruent Segments:


Properties of equilateral triangles

Properties of Equilateral Triangles

Corollaries:

4.3 A triangle is equilateral if and only if it is equiangular.

4.4 Each angle of an equilateral triangle measures 60°.

60°

60°

60°


Example triangle efg is equilateral and segment eh bisects angle e

Example: Triangle EFG is equilateral, and segment EH bisects angle E

Find the measure of angle 1 and 2:

Solve for X:


Assignments

Assignments:

Classwork: WB pg 51 1-6

Homework: Worksheet 4-6


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