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Section 5.4: Midsegment Theorem

Section 5.4: Midsegment Theorem. Goals. Identify the midsegments of a triangle Use properties of midsegments of a triangle. Anchors. Analyze characteristics and properties of two and three dimensional geometric shapes and demonstrate understanding of geometric relationships

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Section 5.4: Midsegment Theorem

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  1. Section 5.4: Midsegment Theorem Goals • Identify the midsegments of a triangle • Use properties of midsegments of a triangle Anchors • Analyze characteristics and properties of two and three dimensional geometric shapes and demonstrate understanding of geometric relationships • Identify and/or use properties of triangles

  2. Using Midsegments of a  • Midsegment of a  A E D C B F

  3. E D F Theorem 5.9: Midsegment Theorem • The midsegment of a  is DE || BC and DE = EF || AB and EF = DF || AC and DF =

  4. D E F AB = 8 , AC = 12 , BC = 14 Find the perimeter of ABC. Find the perimeter of DEF. The perimeter of a triangle formed by the midsegments is

  5. 75 108 DAE = 75, BDE = 108 Find the missing angles in the figure. Explain how you found the missing angles.

  6. The midpoints of the sides of a  are J (-3 , 4) , K (1 , 10) , and L (0 , 5). What are the coordinates of the vertices of the ? Graph it.

  7. The midpoints of the sides of a  are A (8 , 4) , B (4 , 6) , and C (10 , 8). What are the coordinates of the vertices of the ? Label them D, E, & F. Graph it. Use the slope of each midsegment to find the parallel line through the other midpoint. Connect all of the parallel lines. What is the perimeter of DEF. (Round to one decimal place) The perimeter of DEF ≈

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