TEST: Triangle Inequality UNIT 5 11.21.24

Front

Can the sides of a triangle have lengths 3, 4, and 9?

Back

No, because the sum of the lengths of the two shorter sides (3 + 4 = 7) must be greater than the length of the longest side (9).

Front

If the given side lengths of a triangle are 16 and 10, what cannot be the third side? Options: 25, 22, 27, 21

Back

27, because the sum of the two shorter sides (16 + 10 = 26) must be greater than the third side.

Front

Will these three sides form a triangle? (Example: 5, 7, 10)

Back

Yes, because the sum of the lengths of any two sides (5 + 7 = 12, 5 + 10 = 15, 7 + 10 = 17) is greater than the length of the third side.

Front

What is the smallest side? Options: EF, FG, EG

Back

EG, assuming EF, FG, and EG are lengths with EG being the shortest.

Front

What is a possible third side to a triangle with side lengths of 13 and 4? Options: 9, 12, 8, 5

Back

12, because the sum of the two shorter sides (4 + 12 = 16) is greater than the longest side (13).

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 one side of a triangle is 8 and another is 15, what is the range of possible lengths for the third side?

Back

The third side must be greater than |8 - 15| = 7 and less than 8 + 15 = 23. So, the range is (7, 23).

Front

What happens if the sum of two sides equals the third side?

Back

If the sum of two sides equals the third side, the three points are collinear, and they do not form a triangle.

Front

Can a triangle have sides of lengths 5, 5, and 10?

Back

No, because 5 + 5 = 10, which does not satisfy the Triangle Inequality Theorem.

Front

What is the maximum length of the third side if two sides are 6 and 10?

Back

The maximum length of the third side is less than 16 (6 + 10).