5.2 Bisectors of a Triangle Old Vocab: Perp. Bisector, Vertices of a Triangle New: Pythagorean Th., Circumcenter, Incenter

Pythagorean Theorem C is ALWAYS the hypotenuse and A and B are always the legs of the triangle. Find the missing side length. Round any answers to the nearest tenth. 1) 2) 3) 4) ? 8 ? 144 ? ? 3 11 8 4 12

Draw in the three perpendicular bisectors for the following triangles. The point where your lines intersect is called the “point of concurrency”

The point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter.

Concurrency of Perp. Bisectors Th Concurrency of Perp. Bisectors Th. – The perpendicular bisectors of a triangle intersect at a point (the circumcenter) that is equidistant to the vertices of the triangle. A B C The angle bisectors of a triangle meet at a point called the incenter. Draw in the angle bisectors for the following triangles. Label the incenter. A B C

Concurrency of Angle Bisector Th Concurrency of Angle Bisector Th. - The Angle Bisectors of a Triangle intersect at a point (the incenter) that is equidistant from the sides (dropped at a perp. angle) A B C

If 3 or more lines intersect at a point, that point is called the _________? The perpendicular bisectors of a triangle intersect at a point called the ___________ which is equidistant to the ______________ of the triangle. The angle bisectors of a triangle intersect at a point called the ___________ which is equidistant to the ____________ of the triangle. 5) 6) 7)