Triangle Midsegment and Triangle Inequality Theorem

Front

What is the Triangle Midsegment Theorem?

Back

The Triangle Midsegment Theorem states that a segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

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

If two sides of a triangle measure 4 and 12, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 8 and less than 16.

Front

Identify the relationship between the midsegment and the third side in a triangle.

Back

The midsegment is parallel to the third side and is half its length.

Front

If DE is a midsegment of triangle ABC, what can be said about DE and BC?

Back

DE is parallel to BC and DE = 1/2 BC.

Front

What is the shortest side in a triangle with sides QP, QM, and MP if QM is the shortest?

Back

QM is the shortest side.

Front

How do you determine if a triangle can exist with given side lengths?

Back

Use the Triangle Inequality Theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If the sides of a triangle are 5, 7, and x, what is the range of x?

Back

x must be greater than 2 and less than 12.

Front

What is the smallest angle in a triangle with angles ∠J, ∠K, and ∠L if ∠J is the smallest?

Back

∠J is the smallest angle.

Front

If a triangle has sides measuring 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.