Triangle Midsegments and Triangle Inequalities

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

Front

If a triangle has sides of lengths 3, 4, and 5, can it exist?

Back

Yes, it can exist. This satisfies the triangle inequality theorem.

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 LN = 5, what is the length of AC if LN is a midsegment?

Back

AC = 10, because the length of the midsegment is half the length of the opposite side.

Front

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

Back

A midsegment is parallel to the third side and its length is half the length of that side.

Front

Can a triangle have sides of lengths 4, 6, and 10?

Back

No, it cannot exist because 4 + 6 is not greater than 10.

Front

If TS is a midsegment of triangle GHI, and TS = 4, what is the length of side GH?

Back

GH = 8, because 2(midsegment) = opposite side.

Front

What segments are parallel to each other in a triangle with midsegments?

Back

The midsegments are parallel to the sides of the triangle they do not touch.

Front

How do you find the length of a midsegment?

Back

To find the length of a midsegment, take half the length of the side it is parallel to.

Front

If segment NP is a midsegment, what can be said about segments EF and NP?

Back

Segment NP is parallel to segment EF.