Triangle Inequality

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

If a triangle has sides of lengths 7, 10, and x, what is the range of possible values for x?

Back

x must be greater than 3 and less than 17 (3 < x < 17).

Front

In triangle ABC, if angle A is the smallest angle, which side is the shortest?

Back

Side BC is the shortest side.

Front

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

Back

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

Front

If the lengths of two sides of a triangle are 5 and 12, what is the maximum possible length of the third side?

Back

The maximum possible length of the third side is 16 (5 + 12 - 1).

Front

What is the minimum possible length of the third side if the other two sides are 5 and 12?

Back

The minimum possible length of the third side is 7 (12 - 5 + 1).

Front

How do you determine if three lengths can form a triangle?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.

Front

If a triangle has sides of lengths 8, 15, and 20, does it satisfy the Triangle Inequality Theorem?

Back

Yes, it satisfies the theorem because 8 + 15 > 20, 8 + 20 > 15, and 15 + 20 > 8.

Front

What is the significance of the longest side in a triangle?

Back

The longest side is opposite the largest angle in the triangle.

Front

In triangle XYZ, if angle Y is 90 degrees, what type of triangle is it?

Back

It is a right triangle.