1. 6-4: Isosceles Triangles

2. 6-4: Isosceles Triangles
NO NEED TO COPY
Recall from 5-1 that an isosceles triangle has at least two congruent sides.
There are two theorems dealing with isosceles triangles

3. 6-4: Isosceles Triangles
Theorem 6-2: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

4. 6-4: Isosceles Triangles
Theorem 6-3: The median from the vertex angle of an isosceles triangle IS ALSO the perpendicular bisector of the base AND IS ALSO the angle bisector of the vertex angle.

5. 6-4: Isosceles Triangles
Example
Find the value of each variable in isosceles triangle DEF if EG is an angle bisector.
Ignore the bisector for a second…
This is an isosceles triangle
Angles opposite equal sides are equal
x = 49
Bring the bisector back in
The angle bisector of an isosceles triangle is also the perpendicular bisector
y = 90

6. 6-4: Isosceles Triangles
Your Turn
Find the value of the variables in each triangle
x = 65˚
y = 50˚
x = 90˚
y = 70˚

7. 6-4: Isosceles Triangles
Theorem 6-4: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

8. 6-4: Isosceles Triangles
Example
In ABC, A  B and mA = 48.
Find mC, AC, and BC.
Finding mC
A  B, so B also equals 48.
180˚ in a triangle.
C = 180
96 + C = 180
C = 84

9. 6-4: Isosceles Triangles
Example
In ABC, A  B and mA = 48.
Find mC, AC, and BC.
Finding AC & BC
This is an isosceles triangle, so the two marked sides are equal.
4x = 6x – 5
-2x = -5
x = 5/2 (or 2.5)
Plug back in to get AC/BC
AC = 4(2.5) = 10 BC = 6(2.5) – 5 = 10

10. 6-4: Isosceles Triangles
Theorem 6-5: A triangle is only equilateral if it is equiangular

11. 6-4: Isosceles Triangles
Assignment
Study Guide #6-4 and Practice Masters #6-4