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5.1 Bisector, Medians, and Altitudes. B. Theorem 5.1: If a point lies on the perpendicular bisector of a segment, then the point is equidistant from.

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Presentation on theme: "5.1 Bisector, Medians, and Altitudes. B. Theorem 5.1: If a point lies on the perpendicular bisector of a segment, then the point is equidistant from."— Presentation transcript:

1 5.1 Bisector, Medians, and Altitudes

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4 B. Theorem 5.1: If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. 6x - 53x + 16 A BC D Example 1:Find x, if AD is a perpendicular bisector.

5 C. Theorem 5.3: Circumcenter Theorem The circumcenter of a triangle is equidistant from the vertices of the triangle. A B C E Example 2 Find x and y, if BE = 24, AE = 3x – 6 and CE = 5y + 4

6 D. Theorem 5.4: If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle. A B C D Example 3 Find x, if AC is an angle bisector of DAB and DC = x + 4 and BC = 2x – 5.

7 E. Theorem 5.7: Centroid Theorem The distance from the vertex to the point of concurrency is equal to 2 times the distance from the point of concurrency to the midpoint of the opposite side. Example 4 Point A is a centroid of DEF. Find x, y, and z. D S E T FU A SA = 4z EA = y TA = 2x – 5 FA = 4.6 UA = 2.9 DA = 6

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