1. Isosceles Triangles

2. Base Angles Theorem Base angle Base angle
If two sides of a triangle are congruent, then the base angles are also congruent.
Base angles are the angles at the ends of the 2 congruent segments.
So, in the diagram angles B and C are congruent.
Base angle
Base angle

3. Converse of base angles theorem
If two angles in a triangle are congruent, then the triangle is an isosceles triangle.
That means that the 2 sides of the triangles are also congruent.

4. This is an isosceles triangle, so the 2 sides are congruent…
5x + 5 = 35
5x = 30
x = 6

5. Find the value of x
This is an isosceles triangle, so the 2 angles are congruent…
9x = 72
x = 8

6. Find the value of x
x + x = 180
2x = 180
2x = 78
x = 39

7. The sum of the interior angles is 180… x + 7 = 55
Find the value of x
The sum of the interior angles is 180…
x + 7 = 55
x = 48
y = 180
Now find y
110 + y = 180
y = 170

8. Find x and y
x = 9y
9y = 45
y =5
hmmm……
90 + x + x = 180
90 + 2x = 180
2x = 90
x = 45