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Prove and use properties of triangle midsegments.

Objective. Prove and use properties of triangle midsegments. __________________ – a perpendicular segment from a vertex to the line containing the opposite side. Every triangle has three altitudes . An altitude can be inside, outside, or on the triangle.

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Prove and use properties of triangle midsegments.

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  1. Objective Prove and use properties of triangle midsegments.

  2. __________________– a perpendicular segment from a vertex to the line containing the opposite side. Every triangle has three altitudes. An altitude can be inside, outside, or on the triangle.

  3. ________________– a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. Every triangle has three medians.

  4. ____________________– a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

  5. The vertices of ∆XYZ are X(–1, 8), Y(9, 2), and Z(3, –4). M and N are the midpoints of XZ and YZ. Show that and . Example 1: Examining Midsegments in the Coordinate Plane Step 1 Find the coordinates of M and N.

  6. Step 2 Compare the slopes of MN and XY. Example 1 Continued

  7. Step 3 Compare the heights of MN and XY. Example 1 Continued

  8. The relationship shown in Example 1 is true for the three midsegments of every triangle.

  9. Example 2a Find each measure. JL

  10. Example 2b Find each measure. PM

  11. Example 2c Find each measure. mMLK

  12. Example 3: Indirect Measurement Application In an A-frame support, the distance PQ is 46 inches. What is the length of the support ST if S and T are at the midpoints of the sides?

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