1. Triangle Midsegment Theorem
Lesson 55 Saxon Geometry

2. Warm-up Problems: Puzzle Packet

3. Puzzle Packet

4. Essential Questions What is a midsegment of a triangle?
Which of the side lengths of a triangle is the midsegment’s length half of?
Which of the side lengths of a triangle is the midsegment parallel to?
How is a midsegment triangle related to the original triangle?

5. 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.

6. Triangle Midsegment Theorem

7. Using the Triangle Midsegment Theorem
In the diagram, DE is a midsegment of  ABC. Find the values of x and y.

8. Your Turn: Using Triangle Midsegment Thm
In the diagram, PQ is a midsegment of  LMN. Find the values of x and y.

9. Theorem 55-2

10. In the diagram, what are the values of a and b?
Using Theorem 55-2
In the diagram, what are the values of a and b?

11. 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.

12. 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.

13. Applying Similarity to Midsegment Problems
Triangle STU is the midsegment triangle of  PQR.
a. Show that STU ∼ PQR.
b. Find PQ.

14. Your Turn! Applying Similarity
Triangle NOP is the midsegment triangle of  KLM.
a. Show that KLM ∼ NOP.
b. Find the length of LK.

15. Video Summarizer

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

17. Exit Slip
p. 366 #15 & #30
Individual Assessment