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 scissors Draw a 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 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 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

In ∆DEF, A, B and C are midpoints. Name pairs of parallel segments. Example 1 F C

In ∆EFG, H, J and K are midpoints In ∆EFG, H, J and K are midpoints. EF = 60, EG = 100 and HK = 40 Find HJ, JK, and FG. F HJ= J JK= H FG= E K G Example 2

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. A E B More examples D 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?

AB = 10 and CD = 18. Find EB, BC and AC AB = 10 and CD = 18. Find EB, BC and AC. Using the triangle, if EB = 2x and DC = 24, find the value of x. A E B More examples D C

5-1 wkst Homework