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Section 5.1: Midsegments of Triangles PowerPoint Presentation

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)?

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

- 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

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

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

MidsegmentTriangle midpoint L.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

E midpoint L.

A

B

E

Example 1F

C

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

F midpoint L.

HJ=

J

JK=

H

FG=

E

K

G

Example 2In ∆EFG, H, J and K are midpoints.

EF = 60, EG = 100 and HK = 40

Find HJ, JK, and FG.

A midpoint L.

E

B

More examplesD

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.

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?

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