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

Back

The length of the third side must be greater than 2 cm and less than 12 cm, so the range is 2 < x < 12.

Front

Can the lengths 3 cm, 4 cm, and 8 cm form a triangle?

Back

No, because 3 + 4 is not greater than 8.

Front

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

Back

1. Equilateral: all sides are equal. 2. Isosceles: two sides are equal. 3. Scalene: all sides are different.

Front

What are the three types of triangles based on angles?

Back

1. Acute: all angles are less than 90 degrees. 2. Right: one angle is exactly 90 degrees. 3. Obtuse: one angle is greater than 90 degrees.

Front

If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, is it a right triangle?

Back

Yes, because 6^2 + 8^2 = 10^2 (36 + 64 = 100).

Front

What is the minimum length of a side of a triangle if the other two sides are 10 cm and 15 cm?

Back

The minimum length must be greater than 5 cm (10 - 15 < x).

Front

What is the maximum length of a side of a triangle if the other two sides are 10 cm and 15 cm?

Back

The maximum length can be less than 25 cm (10 + 15 > x).

Front

Identify the triangle with sides 5 cm, 5 cm, and 8 cm.

Back

This is an Isosceles triangle because two sides are equal.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.