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Chapter 5 Relationships Within Triangles

Chapter 5 Relationships Within Triangles. Section 5 – 1 Midsegments of Triangles. Objective: To use properties of midsegments to solve problems. Midsegment of a Triangle :. A segment connecting the midpoints of two sides. Theorem 5 – 1 Triangle Midsegment Theorem.

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Chapter 5 Relationships Within Triangles

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  1. Chapter 5Relationships Within Triangles

  2. Section 5 – 1Midsegments of Triangles Objective: To use properties of midsegments to solve problems

  3. Midsegment of a Triangle: A segment connecting the midpoints of two sides.

  4. Theorem 5 – 1 Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length.

  5. Proving Theorem 5 – 1 • Use the Midpoint Formula to find the coordinates of R and S.

  6. Proving Theorem 5 – 1 • Prove that

  7. Proving Theorem 5 – 1 • Prove RS is ½ of OQ.

  8. Example 1 Finding Lengths A) In ∆EFG, H, J, and K are midpoints. Find HJ, JK, and FG.

  9. B) AB = 10 and CD = 18. Find EB, BC, and AC. C) In ∆XYZ, M, N, and P are midpoints. The perimeter of ∆MNP is 60. Find NP and YZ.

  10. Example 2 Identifying Parallel Segments A) In ∆DEF, A, B, and C are midpoints. Name pairs of parallel segments.

  11. B) Find m VUZ. C) Find m AMN and m ANM.

  12. Example 3 Real-World Connection A) Dean plans to swim the length of the lake, as shown in the photo. How far would Dean swim? Here is a diagram that illustrates what Dean did:

  13. B) is a new bridge being built over a lake as shown. Find the length of the bridge. C) How long is the bridge in miles?

  14. Textbook Page 246 – 247; #2 – 36 Even

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