Section 5 1 midsegments of triangles
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Section 5.1: Midsegments of Triangles

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Section 5 1 midsegments of triangles

Warmup: 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 (write your answer in x ft., y in., guess if you don’t know)?


Section 5 1 midsegments of triangles

Section 5.1: Midsegments of Triangles

LEQ: What is a midsegment of a triangle and how can it help us solve problems?


Section 5 1 midsegments of triangles

  • Need a sheet of paper, ruler, and scissors

  • Draw a scalene triangle and cut it out

  • Label the vertices A,B, and C

  • Measure AB and record your measurement

B

A

C


Section 5 1 midsegments of triangles

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 LN

4.) measure LN.

5.) How does this compare AB?

B

A

C

L


Midsegment

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

Midsegment


Section 5 1 midsegments of triangles

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

E

A

B

E

Example 1

F

C

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


Example 2

F

HJ=

J

JK=

H

FG=

E

K

G

Example 2

In ∆EFG, H, J and K are midpoints.

EF = 60, EG = 100 and HK = 40

Find HJ, JK, and FG.


More examples

A

E

B

More examples

D

C

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

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


Section 5 1 midsegments of triangles

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?


Homework

  • 5.1 wkst

Homework


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