Isosceles Triangles

Front

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length and the angles opposite those sides are also equal.

Front

What are the properties of an isosceles triangle?

Back

1. Two sides are equal in length. 2. The angles opposite the equal sides are equal. 3. The altitude from the vertex angle bisects the base.

Front

If the base angles of an isosceles triangle are both 40°, what is the measure of the vertex angle?

Back

100°

Front

In an isosceles triangle, if one base angle is 70°, what is the measure of the other base angle?

Back

70°

Front

What is the formula to find the vertex angle of an isosceles triangle given the base angles?

Back

Vertex angle = 180° - 2 * (base angle).

Front

How do you identify the base of an isosceles triangle?

Back

The base of an isosceles triangle is the side that is not equal in length to the other two sides.

Front

If the lengths of the equal sides of an isosceles triangle are 10 cm each and the base is 12 cm, what is the height of the triangle?

Back

Using the Pythagorean theorem, height = √(10² - (12/2)²) = √(100 - 36) = √64 = 8 cm.

Front

What is the relationship between the angles in an isosceles triangle?

Back

The angles opposite the equal sides are equal, and the sum of all angles in any triangle is 180°.

Front

If an isosceles triangle has a vertex angle of 40°, what are the measures of the base angles?

Back

Each base angle measures 70°.

Front

What is the significance of the altitude in an isosceles triangle?

Back

The altitude from the vertex angle to the base bisects the base and creates two congruent right triangles.