Triangle Midsegments

Triangle Midsegments and Proportionality
(You may want a calculator)

Multiple Select

DE is a midsegment. Based off the image, which statements are true? Select all that apply.

• D is a midpoint of AB

• E is a midpoint of AC

• DE = BC

• DE is parallel to BC

​If a segment joins the midpoints of two sides of a triangle,

the segment is parallel to the third side
and
the segment is half as long as the third side

Triangle Midsegment Theorem:

Fill in the Blanks

Given M, N midpoints.
MN = 12
Find DF.

Fill in the Blanks

Given D, E midpoints.
DE = 3x - 5
BC = 26
Find x.

Multiple Choice

Find the length of PQ

• 30

• 60

• 7

• 15

• 16

Multiple Choice

Find the length of PU

• 32

• 64

• 7

• 14

• 16

• If a line parallel to the side of a triangle intersects the other two sides, THEN it divides those sides proportionally.

​

Triangle Proportionality Theorem

Fill in the Blanks

Find the value of x.

SOLUTION:
There is more than one way to set up your proportion!

In order to compare the parallel sides, you must set up the proportion comparing Big and Small triangles

​

​CAUTION!!

Fill in the Blanks

Solve for the missing value

Multiple Choice

Solve for the missing value

• 60/14

  (reduced 30/7)

• 6

• 5

• 10

Fill in the Blanks

Solve for x.