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Chapter 5: Relationships within Triangles

Chapter 5: Relationships within Triangles. 5.1 Midsegments of Triangles. Activity. I will give you a triangle and a ruler. (obtuse, acute, or right) The vertices are labeled for you. Fold angle A onto angle C to find the midpoint of AC. Label it L.

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Chapter 5: Relationships within Triangles

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  1. Chapter 5: Relationships within Triangles 5.1 Midsegments of Triangles

  2. Activity • I will give you a triangle and a ruler. (obtuse, acute, or right) The vertices are labeled for you. • Fold angle A onto angle C to find the midpoint of AC. Label it L. • Fold angle B onto angle C to find the midpoint of BC. Label it N. • How does LN compare to AB?

  3. Activity • Make a conjecture about how the segment joining the midpoints of two sides of a triangle is related to the third side of the triangle.

  4. Midsegments • a segment connecting the midpoints of two sides of a triangle

  5. 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.

  6. Example 1 • In ΔEFG, H, J, and K are midpoints. Find HJ, JK, and FG. 60 100

  7. Example 1a • AB = 10 and CD = 18. Find EB, BC, and AC.

  8. Example 2 • In ΔDEF, A, B, and C are midpoints. Name pairs of parallel segments.

  9. Example 2a • Find the measure of angle VUZ. Justify your answer.

  10. Example 3 • a. CD is a new bridge being built over a lake as shown. Find the length of the bridge. • b. How long is the bridge in miles?

  11. Homework

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