Isosceles and Equilateral 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 equal.

Front

What is an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length and all three angles are equal, each measuring 60 degrees.

Front

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

Back

In an isosceles triangle, the angles opposite the equal sides are equal. To find the angles, use the fact that the sum of all angles in a triangle is 180 degrees.

Front

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

Back

The vertex angle is 90 degrees, since 45 + 45 + 90 = 180.

Front

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

Back

In an equilateral triangle, all sides are equal, and all angles are equal to 60 degrees.

Front

How do you calculate the height of an isosceles triangle?

Back

The height can be calculated using the Pythagorean theorem. If 'b' is the base and 'a' is the length of the equal sides, the height 'h' is given by h = √(a² - (b/2)²).

Front

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

Back

The area A of an equilateral triangle with side length 's' is given by A = (√3/4) * s².

Front

If two angles of a triangle are 70 degrees each, what type of triangle is it?

Back

It is an isosceles triangle, as it has at least two equal angles.

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of any triangle is always 180 degrees.

Front

In an isosceles triangle, if one angle measures 30 degrees, what are the measures of the other two angles?

Back

The other two angles each measure 75 degrees, since 30 + 75 + 75 = 180.