NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3. Any point that is on the perpendicular bisector of a segment is equidistant from the endpoints of the.

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Presentation transcript:

NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

Any point that is on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment. Any point on the angle bisector is equidistant from the sides of the angle. Remember, distance is always measured on the perpendicular. Any point equidistant from the sides of an angle lies on the angle bisector. If PM = PN, then is an angle bisector. M N A C B P D M N A C B P D If is an angle bisector, then PM = PN

Definitions Point of Concurrency - A common point in which three or more lines intersect Circumcenter - The intersection point of the three perpendicular bisectors of a triangle Incenter - The intersection point of the three angle bisectors of a triangle Centroid - The intersection point of the three medians of a triangle Orthocenter - The intersection point of the three altitudes of a triangle

Theorems Circumcenter Theorem- The circumcenter of a triangle is equidistant from the vertices of the triangle Incenter Theorem- The incenter of a triangle is equidistant from each side of the triangle Centroid Theorem- The centroid of a triangle is two-thirds the distance of its corresponding median of the triangle

Example 1-2a ALGEBRA Points U, V, and W are the midpoints of respectively. Find a, b, and c. Find a. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 14.8 from each side. Divide each side by 4.

Example 1-2a Find b. Segment Add Postulate Centroid Theorem Find c. Segment Addition Postulate Centroid Theorem

ALGEBRA Points T, H, and G are the midpoints of respectively. Find w, x, and y. Example 1-2b Answer:

HW : Page 242