Isosceles Triangle Theorem

Front

What is the Isosceles Triangle Theorem?

Back

The Isosceles Triangle Theorem states that in an isosceles triangle, the angles opposite the equal sides are equal.

Front

How do you find the measure of the angles in an isosceles triangle?

Back

To find the measure of the angles in an isosceles triangle, you can use the fact that the sum of the angles in any triangle is 180 degrees. If two angles are equal, you can set them as 'x' and solve for 'x'.

Front

If two angles of an isosceles triangle are 60 degrees each, what is the measure of the third angle?

Back

The third angle would be 60 degrees because the sum of the angles in a triangle is 180 degrees (60 + 60 + x = 180, so x = 60).

Front

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

Back

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

Front

If one angle of an isosceles triangle is 80 degrees, what are the measures of the other two angles?

Back

The other two angles would each measure 50 degrees because the sum of the angles must equal 180 degrees (80 + 2x = 180, so 2x = 100, thus x = 50).

Front

How can you determine if a triangle is isosceles?

Back

A triangle is isosceles if at least two of its sides are of equal length.

Front

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

Back

The area of an isosceles triangle can be calculated using the formula: Area = (base * height) / 2.

Front

In an isosceles triangle, if the equal sides are each 10 units long and the base is 8 units long, what is the height?

Back

You can use the Pythagorean theorem to find the height. The height divides the base into two equal segments of 4 units each. Using the formula: height = √(10^2 - 4^2) = √(100 - 16) = √84, which is approximately 9.17 units.

Front

What is the significance of the vertex angle in an isosceles triangle?

Back

The vertex angle is the angle formed by the two equal sides of the isosceles triangle, and it is unique compared to the base angles.

Front

If the base angles of an isosceles triangle are each 45 degrees, what is the vertex angle?

Back

The vertex angle would be 90 degrees because the sum of the angles in a triangle is 180 degrees (45 + 45 + x = 180, so x = 90).