Midsegments of Triangles

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Presentation transcript:

Midsegments of Triangles

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

Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Angle Bisector Theorem If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Converse of the Angle Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

In XYZ, M, N, and P are midpoints. The perimeter of MNP is 60 In XYZ, M, N, and P are midpoints. The perimeter of MNP is 60. Find NP and YZ.

Find x, FB, and FD in the diagram above. FD = FB Angle Bisector Theorem 7x – 37 = 2x + 5 Substitute. 7x = 2x + 42 Add 37 to each side. 5x = 42 Subtract 2x from each side. x = 8.4 Divide each side by 5. FB = 2(8.4) + 5 = 21.8 Substitute. FD = 7(8.4) – 37 = 21.8 Substitute.

Assignment P 262 #1-12 P 267 #1-4, 6-26