The triangular face of the Rock and Roll Hall of Fame in Cleveland, Ohio, is isosceles. The length of the base is 229ft. 6 in. What is the length of the highlighted line that lies at the halfway point of both legs of the triangle?

Section 5.1: Midsegments of

Triangles LEQ: What is a midsegment of a triangle and how can it

help us solve problems?

Need a sheet of paper, ruler, and scissorsDraw a triangle and cut it outLabel the vertices A,B, and CMeasure AB and record your

measurement

A C

B

1.) Fold A onto C to find the midpoint of AC. Label the midpoint L.

2.) Fold B onto C to find the midpoint of BC and label it N

3.) construct line LN4.) measure LN.5.) How does this compare AB?

A C

B

L

Midsegment

A midsegment of a triangle is a segment connecting the midpoints of 2 sides.

Triangle midsegment theorem:“If a segment joins the midpoints of 2 sides

of a triangle, then the segment is parallel to the third side, and is half its length.”

R Q

Example 1

In ∆DEF, A, B and C are midpoints. Name pairs of parallel segments.

E

EF

A

C

B

Example 2

In ∆EFG, H, J and K are midpoints.EF = 60, EG = 100 and HK = 40 Find HJ, JK, and FG.

F

JH

EK G

HJ=

JK=

FG=

More examples

AB = 10 and CD = 18. Find EB, BC and AC. Since AB=BC and EA=ED, E and B are midpoints, making

EB a midsegment.

Using the triangle, if EB = 2x and DC = 24, find the value of x.

D

E

A

B

C

The triangular face of the Rock and Roll Hall of Fame in Cleveland, Ohio, is isosceles. The length of the base is 229ft. 6 in. What is the length of the highlighted line that lies at the halfway point of both legs of the triangle?

More examples

AB = 10 and CD = 18. Find EB, BC and AC.

Using the triangle, if EB = 2x and DC = 24, find the value of x.

D

E

A

B

C

Homework

5-1 wkst