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Mastering Triangle Midsegment Theorem - Lesson 55 Geometry

Dive into the concept of midsegments of triangles in Saxon Geometry Lesson 55. Explore theorem applications, identifying midpoints, and applying similarity to solve problems. Engage with practice questions and an exit slip for individual assessment.

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Mastering Triangle Midsegment Theorem - Lesson 55 Geometry

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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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