Midsegment Theorem

Front

What is the Midsegment Theorem?

Back

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

Front

If AB is the third side of triangle ABC, and D and E are midpoints of AC and BC respectively, what is the length of DE if AB = 20?

Back

DE = 10 (since DE is half of AB).

Front

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

Back

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

Front

How do you find the length of a midsegment in a triangle?

Back

To find the length of a midsegment, measure the length of the side it is parallel to and divide by 2.

Front

If the midsegment DE of triangle ABC is 9, what is the length of side AB?

Back

AB = 18 (since DE is half of AB).

Front

What are the coordinates of the midpoints D and E if A(2, 4) and B(6, 8) are vertices of triangle ABC?

Back

D = (4, 6) and E = (3, 5) if C is at (0, 0).

Front

In triangle XYZ, if XY = 14 and the midsegment connecting the midpoints of XZ and YZ is 7, what does this tell you?

Back

This confirms the Midsegment Theorem, as the midsegment is half the length of the side XY.

Front

What is the significance of the Midsegment Theorem in geometry?

Back

It helps in solving problems related to triangle properties and relationships between sides.

Front

If the lengths of sides AC and BC are 12 and 16 respectively, what is the length of the midsegment DE?

Back

DE = 8 (since DE is half of the length of side AB, which is 16).

Front

What is the formula for the length of a midsegment in a triangle?

Back

Length of midsegment = 1/2 * length of the side it is parallel to.