2. Isosceles Triangles
Sec: 4.6
Sol: G.5

3. 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. 3
Leg
Base 2 1
Vertex
Base Angles

4. Theorem 4.9 Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides (base angles) are congruent. A B C

5. Given: Prove:
Statement
Reason 1. 2. 3. 4. 5.

6. Find the measure of the missing angle
If What is the measure of

7. Lesson 3-2: Isosceles Triangle
Theorem 4.10
If two angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C
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 50
3x - 7
x+15 A B C
Lesson 3-2: Isosceles Triangle

8. Example:
Name Two Congruent Angles:
Name Two Congruent Segments:

9. 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°

10. Example: Triangle EFG is equilateral, and segment EH bisects angle E
Find the measure of angle 1 and 2: Solve for X:

11. Assignments:
Classwork: WB pg Homework: Worksheet 4-6