Triangle Midsegment Theorem

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Presentation transcript:

Triangle Midsegment Theorem Lesson 55 Saxon Geometry

Warm-up Problems: Puzzle Packet

Puzzle Packet

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?

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

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?

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