Triangle Inequality and Different Types of Triangles

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What are the three types of triangles based on side lengths?

Back

1. Equilateral Triangle: All sides are equal. 2. Isosceles Triangle: Two sides are equal. 3. Scalene Triangle: All sides are different.

Front

What are the three types of triangles based on angles?

Back

1. Acute Triangle: All angles are less than 90 degrees. 2. Right Triangle: One angle is exactly 90 degrees. 3. Obtuse Triangle: One angle is greater than 90 degrees.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a Right Triangle.

Front

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

Back

The vertex angle is equal to 180 degrees minus twice the measure of one of the base angles.

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 degrees.

Front

If the lengths of two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 (5 - 7) and less than 12 (5 + 7). So, it must be between 2 and 12.

Front

What is an equiangular triangle?

Back

An equiangular triangle is a triangle in which all three angles are equal, and therefore, all three sides are also equal.

Front

How do you classify a triangle with sides measuring 3, 4, and 5?

Back

It is a Scalene Triangle because all sides are of different lengths.

Front

What is the relationship between the sides and angles of a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.