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Triangle Midsegment Theorem

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?

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Triangle Midsegment Theorem

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  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. 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

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