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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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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.
________________– a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. Every triangle has three medians.
____________________– a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.
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.
Step 2 Compare the slopes of MN and XY. Example 1 Continued
Step 3 Compare the heights of MN and XY. Example 1 Continued
The relationship shown in Example 1 is true for the three midsegments of every triangle.
Example 2a Find each measure. JL
Example 2b Find each measure. PM
Example 2c Find each measure. mMLK
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?