Triangle Midsegment

Triangle Midsegment Theorem

Dr. Tom Giles

Special Segments in Triangles

Perpendicular Bisector, Angle Bisector, Median, Altitude, Mid-segment

Midsegment of a Triangle

​In an isosceles triangle, the angle bisector, perpendicular bisector, median, and altitude drawn from the vertex angle to the base are all the same segment.

In an equilateral triangle, this is true from any angle.

Multiple Choice

Is DE parallel to BC?

• yes

• no

Multiple Choice

Is DE half the length of BC?

• yes

• no

Use the Midsegment Theorem to Find Lengths

Construction: Triangles are used for strength in roof trusses. In the diagram, UV and VW are midsegments of Triangle RST. Find UV and RS. Solution on next slide.

Find UV & RS.

UV = 1/2 * RT = 1/2 (90 in. ) = 45 in

RS = 2 * VW = 2(57 in.) = 114 in.

Multiple Choice

What is the length of AB?

• 4

• 8

• 16

• 24

Multiple Choice

Find the length of the segment.

• 5

• 5/2

• 10

Multiple Choice

What is the value of x?

• 10

• 5

• 2

• no solution

Multiple Choice

Find v.

• 33

• 66

• 2v + 66

• v + 33

Multiple Choice

Find T.

• 35

• 5

• 40

• 4.5

Reminder!!!

DE = 1/2(AB)

CE = BE

AD = DC

Multiple Choice

If CE = 12, what is the value of CB?

• 12

• 6

• 24

Multiple Choice

What is the value of y?

• 3

• -3

• 5

• no solutoin

Midsegment of a Triangle

Multiple Choice

WINDOWS: A large triangular window is segmented as shown. In the diagram, DF and EF are midsegments of triangle ABC. Find DF.

• 45

• 90

• 180

Multiple Choice

WINDOWS: A large triangular window is segmented as shown. In the diagram, DF and EF are midsegments of triangle ABC. Find AB.

• 45

• 90

• 180

Multiple Choice

Suppose UW = 81, find ST.

• 81

• 40.5

• 162

Let's Review

Multiple Choice

The figure is an example of a(n) ...

• angle bisector

• perpendicular bisector

• median

• midsegment

Multiple Choice

The figure is an example of a(n) ...

• altitude 

• perpendicular bisector

• midsegment

• angle bisector

Multiple Choice

Which of the following segments represents an altitude?

• BX

• AZ

• AC

• BZ

Multiple Choice

Identify the type of segment pictured below.

• Midsegment

• Median

• Altitude

• Perpendicular Bisector

• Angle Bisector

Multiple Choice

What is m $$m\angle SQP$$ and $$m\angle PQR$$

• m∠SQP=29, m∠PQR=58

• m∠SQP=29, m∠PQR=29

• m∠SQP=58, m∠PQR=58

• m∠SQP=58, m∠PQR=29

Multiple Choice

Which of the following words describes the point shown in the figure?

• Centerpoint

• Orthocenter

• Centroid

• Altitude-point

Multiple Choice

The figure is an example of a(n) ...

• median

• altitude

• midsegment

• angle bisector

Match

Match each problem with the correct answer.

• The value of x

• The value of x

• The length of AB

6

13

15

• 6

• 13

• 15