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 is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180°.

Front

If the base angles of an isosceles triangle are equal, what can be said about the vertex angle?

Back

The vertex angle can be found by subtracting the sum of the base angles from 180°.

Front

In an isosceles triangle with base angles of 40°, what is the measure of the vertex angle?

Back

The vertex angle is 100°.

Front

If one angle of an isosceles triangle is 30°, what are the measures of the other two angles?

Back

The other two angles are each 75°.

Front

How do you find the length of the equal sides of an isosceles triangle given the base and the vertex angle?

Back

Use the formula: length = (base/2) / cos(vertex angle/2).

Front

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

Back

In an isosceles triangle, the angles opposite the equal sides are equal.

Front

If 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

The height can be found using the Pythagorean theorem: height = √(10² - (12/2)²) = 8 cm.

Front

What is the formula for the area of an isosceles triangle?

Back

Area = (base * height) / 2.

Front

If the height of an isosceles triangle is 6 cm and the base is 10 cm, what is the area?

Back

Area = (10 * 6) / 2 = 30 cm².