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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? - PowerPoint PPT Presentation
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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