Midsegment Theorem

Front

What is the Midsegment Theorem in a triangle?

Back

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

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle.

Front

If DE is a midsegment of triangle ABC, what can be said about its relationship to side BC?

Back

DE is parallel to BC and its length is half the length of BC.

Front

How do you find the length of a midsegment if you know the lengths of the sides it connects?

Back

The length of the midsegment is equal to half the length of the side it is parallel to.

Front

If AB = 16, what is the length of the midsegment QS in triangle ABC?

Back

QS = 32, since QS is parallel to side AB and is twice the length of AB.

Front

What is the significance of the midpoints in the Midsegment Theorem?

Back

The midpoints are crucial because the midsegment is defined by connecting these points, ensuring the properties of parallelism and proportionality.

Front

Can a triangle have more than one midsegment?

Back

Yes, a triangle has three midsegments, each connecting the midpoints of two sides.

Front

What is the relationship between the lengths of the midsegments in a triangle?

Back

Each midsegment is half the length of the side it is parallel to, maintaining a consistent ratio.

Front

If DE is a midsegment and is parallel to BC, what can be inferred about angles D and B?

Back

Angles D and B are corresponding angles and are therefore equal.

Front

What happens to the properties of the midsegment if the triangle is scaled?

Back

The properties remain the same; the midsegment will still be parallel to the third side and half its length, regardless of the triangle's size.