#6.4 The Triangle Midsegment Theorem

Front

What is the Triangle Midsegment Theorem?

Back

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

Front

If SR is a midsegment of triangle ABC, what is the relationship between SR and side AC?

Back

SR is parallel to side AC and its length is half of the length of AC.

Front

Given that SR = 46, what is the length of side AC?

Back

AC = 2 * SR = 2 * 46 = 92.

Front

If AB = 16, what is the length of QS if QS is a midsegment?

Back

QS = 2 * AB = 2 * 16 = 32.

Front

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

Back

To find the length of a midsegment, take the average of the lengths of the two sides it connects and divide by 2.

Front

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

Back

Midpoints are crucial as the midsegment connects the midpoints of two sides, ensuring the properties of parallelism and proportionality.

Front

If CA = 68, what is the length of the midsegment SR?

Back

SR = CA / 2 = 68 / 2 = 34.

Front

What is the formula to calculate the length of a midsegment given two sides of a triangle?

Back

Midsegment length = (Side 1 + Side 2) / 2.

Front

In triangle ABC, if BR = 23, what is the length of side AB?

Back

AB = 2 * BR = 2 * 23 = 46.

Front

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

Back

The lengths of the midsegments are always half the lengths of the sides they are parallel to.