Triangle Inequality Theorem Practice

Front

What is the Triangle Inequality Theorem?

Back

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

Front

Identify the 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

Identify the types of triangles based on sides.

Back

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

Front

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

Back

The length of the third side must be greater than 2 inches and less than 12 inches.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of AC?

Back

AC must be greater than 7 inches and less than 27 inches.

Front

How do you determine the smallest angle in a triangle?

Back

The smallest angle is opposite the shortest side of the triangle.

Front

List the side measures in order from shortest to longest: 8, 5, 10.

Back

5, 8, 10.

Front

What is an obtuse scalene triangle?

Back

An obtuse scalene triangle has one angle greater than 90 degrees and all sides of different lengths.

Front

If the sides of a triangle are 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side.