Triangle Midsegment Theorem

Lesson 55 Saxon Geometry

Warm-up Problems: Puzzle Packet

Puzzle Packet

Essential Questions

1. What is a midsegment of a triangle?

2. Which of the side lengths of a triangle is the midsegment’s length half of?

3. Which of the side lengths of a triangle is the midsegment parallel to?

4. How is a midsegment triangle related to the original triangle?

New Concepts: Lesson 55

• A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments. The midsegment is always half the length of the side that does not have a midsegment endpoint on it.

Triangle Midsegment Theorem

Using the Triangle Midsegment Theorem

• In the diagram, DE is a midsegment of ABC. Find the values of x and y.

Your Turn: Using Triangle Midsegment Thm

• In the diagram, PQ is a midsegment of LMN. Find the values of x and y.

Theorem 55-2

Using Theorem 55-2

• In the diagram, what are the values of a and b?

Identifying Midpoints of Sides of Triangles

• Triangle MNP has vertices M(-2, 4), N(6, 2), and P(2, -1). QR is a midsegment of MNP. Find the coordinates of Q and R.

Identifying Midpoints of Sides of Triangles

• Triangle ABC has vertices A(-2, 1), B(4, 3), and C(2,-2). DE is a midsegment of ABC parallel to AC . Find the coordinates of D and E.

Applying Similarity to Midsegment Problems

• Triangle STU is the midsegment triangle of PQR.

• a. Show that STU ∼ PQR.• b. Find PQ.

Your Turn! Applying Similarity

• Triangle NOP is the midsegment triangle of KLM.

• a. Show that KLM ∼ NOP.• b. Find the length of LK.

Video Summarizer

Written Practice

• L55 Practice p. 364 a, b, c, d• Please; work with a partner.

Exit Slip

• p. 366 #15 & #30• Individual Assessment