Chapter 5Relationships Within

Triangles

Section 5 – 1Midsegments of

TrianglesObjective:

To use properties of midsegments to solve problems

Midsegment of a Triangle:

A segment connecting the midpoints of two sides.

Theorem 5 – 1Triangle Midsegment Theorem

If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the

third side, and is half its length.

Proving Theorem 5 – 1

• Use the Midpoint Formula to find the coordinates of R and S.

Proving Theorem 5 – 1

• Prove that

Proving Theorem 5 – 1

• Prove RS is ½ of OQ.

Example 1 Finding Lengths

A) In ∆EFG, H, J, and K are midpoints. Find HJ, JK, and FG.

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

C) In ∆XYZ, M, N, and P are midpoints. The perimeter of ∆MNP is 60. Find NP and YZ.

Example 2 Identifying Parallel Segments

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

B) Find m VUZ.

C) Find m AMN and m ANM.

Example 3 Real-World Connection

A) Dean plans to swim the length of the lake, as shown in the photo. How far would Dean swim?

Here is a diagram that illustrates what Dean did:

B) is a new bridge being built over a lake as shown. Find the length of the bridge.

C) How long is the bridge in miles?

Textbook Page 246 – 247; #2 – 36 Even