Midsegment Theorem (line segments)

Front

What is the Midsegment Theorem?

Back

The 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

If a triangle has sides of lengths 10 and 14, what is the length of the midsegment connecting the midpoints of these two sides?

Back

12 (The midsegment is half the length of the third side, which is 24.)

Front

What is the relationship between the lengths of the sides of a triangle and its midsegments?

Back

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

Front

If the midsegment of a triangle is 15 units long, what is the length of the side it is parallel to?

Back

30 units (The side is twice the length of the midsegment.)

Front

In triangle ABC, if D and E are midpoints of sides AB and AC respectively, what can be said about segment DE?

Back

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

Front

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

Back

To find the length of a midsegment, identify the lengths of the two sides it connects, then use the Midsegment Theorem to determine its length.

Front

If the lengths of two sides of a triangle are 20 and 30, what is the maximum possible length of the midsegment connecting these two sides?

Back

25 units (The midsegment is half the length of the third side, which must be less than the sum of the other two sides.)

Front

What is the significance of the Midsegment Theorem in solving triangle problems?

Back

The Midsegment Theorem helps in simplifying problems involving triangles by providing relationships between sides.

Front

If the midsegment of a triangle is 18 units long, what can you conclude about the side it is parallel to?

Back

The side it is parallel to is 36 units long.

Front

In triangle XYZ, if XY = 24 and XZ = 30, what is the length of the midsegment connecting Y and Z?

Back

12 units (The midsegment is half the length of the side opposite to it.)