Midsegments of Triangles

Front

What is a midsegment of a triangle?

Back

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

Front

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

Back

The length of a midsegment is half the length of the third side of the triangle.

Front

If segment AB is a midsegment of triangle ABC, what can be said about segment AC?

Back

Segment AB is parallel to segment AC and its length is half of AC.

Front

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

Back

To find the length of a midsegment, take half the length of the side of the triangle that is not connected to the midsegment.

Front

If the lengths of sides AB and AC are 10 and 14 respectively, what is the length of the midsegment connecting the midpoints of AB and AC?

Back

The length of the midsegment is 7 (half of 14).

Front

What is the significance of midsegments in triangle similarity?

Back

Midsegments create smaller triangles that are similar to the original triangle.

Front

If triangle DEF has midsegment GH, what can be inferred about segments DE and DF?

Back

Segments DE and DF are parallel to segment GH.

Front

What is the relationship between the midsegments of two triangles that are similar?

Back

The midsegments of similar triangles are also proportional to the corresponding sides of the triangles.

Front

If a triangle has sides of lengths 8, 6, and 10, what is the length of the midsegment parallel to the side of length 10?

Back

The length of the midsegment is 5 (half of 10).

Front

In triangle XYZ, if XY = 12 and XZ = 16, what is the length of the midsegment connecting the midpoints of XY and XZ?

Back

The length of the midsegment is 8 (half of 16).