Altitude, perpendicular bisector, both, or neither?

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Presentation transcript:

Altitude, perpendicular bisector, both, or neither? Warm-up E A 1. If CD = 3.25, what is BC? B 6.5 G 2. Find AG if DG = 10. D 20 C 3. If CG = 7, find CE? 10.5 Altitude, perpendicular bisector, both, or neither? PER. BISECTOR NEITHER BOTH ALTITUDE

Perpendicular Bisector 5-2 Perpendicular Bisector perpendicular to a side at its midpoint

Perpendicular Bisector Theorem 5-2 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

How many perpendicular bisectors does a triangle have? The intersection of the perpendicular bisector is called the CIRCUMCENTER. How many perpendicular bisectors does a triangle have?

What is special about the CIRCUMCENTER? Equidistant to the vertices of the triangle.

Example 1: Point G is the circumcenter of the triangle. Find GB. 7 A 7 5 2 B C F 7

Example 2: Point G is the circumcenter of the triangle. Find CG. 10 A 6 B 8 C F 10

cuts the angle into 2 equal parts 5-3 Angle Bisector Angle Bisector cuts the angle into 2 equal parts

The intersection of the angle bisectors is called the INCENTER. How many angle bisectors does a triangle have?

What is special about the INCENTER? Equidistant to sides of the triangle

Example 1: Point N is the incenter of the triangle. Find the length of segment ON. 30 18 18

Example 2: Point N is the incenter of the triangle. Find the length of segment NP. 15