Triangle Inequality Theorem

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

Which side lengths would NOT form a triangle? {3,4,5}, {2,5,9}, {5,10,12}, {7,9,11}

Back

{2,5,9} because 2 + 5 is not greater than 9.

Front

Can the following side measures form a triangle? 3, 5, 8

Back

No, because 3 + 5 is not greater than 8.

Front

Will these side lengths make a triangle? 5 cm, 7 cm, 9 cm

Back

Yes, because 5 + 7 > 9, 5 + 9 > 7, and 7 + 9 > 5.

Front

Identify the shortest side measure from QP, QM, MP if QM = 3 cm, QP = 4 cm, MP = 5 cm.

Back

QM is the shortest side measure.

Front

List the angles in order by measure, smallest to largest: ∠B, ∠A, ∠C

Back

∠A, ∠C, ∠B.

Front

If one side of a triangle is 10 cm and the other two sides are 6 cm and 8 cm, can it form a triangle?

Back

Yes, because 6 + 8 > 10, 6 + 10 > 8, and 8 + 10 > 6.

Front

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

Back

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If a triangle has sides of lengths 7, 24, and 25, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 7 + 24 > 25, 7 + 25 > 24, and 24 + 25 > 7.

Front

What is the minimum length of the third side if two sides of a triangle are 8 cm and 10 cm?

Back

The minimum length of the third side must be greater than 2 cm (10 - 8).