Review Perpendicular and Angle bisectors in Triangles

Review Perpendicular and Angle bisectors in Triangles

*Definitions and properties of special parts of triangles

Perpendicular Bisector

• Is perpendicular to a leg of a triangle

• Passes through the midpoint of that leg

• Is equidistant from the endpoints of that leg

Multiple Choice

The three perpendicular bisectors in a triangle...

• intersect at a point inside the triangle

• intersect at a point equidistant from all three vertices

• intersect at a point equidistant from the sides

• do not intersect at the same point

Multiple Choice

The perpendicular bisectors in a triangle intersect at a point called the ______? *In this picture point P *

• circumcenter

• incenter

• centroid

• vertex

• origin

The Circumcenter

• the point where the perpendicular bisectors intersect

• is equidistant from each vertex

• the center of a circle that can be drawn around the triangle so each vertex lies on the circle

• is inside the triangle (acute), outside the triangle (obtuse), on triangle (right)

Multiple Choice

A triangle is located at the points A(1, 1) B(5, 2) and C(3, 5). What is an equation for the perpendicular bisector of

$$\overline{AC}$$  ?

• $$\frac{1}{2}\left(x\ -\ 2\right)=y-3$$  

• $$y=-\frac{1}{2}x+3$$  

• $$y=-\frac{1}{2}x+4$$  

• $$y-2=2\left(x-3\right)$$  

Open Ended

Suppose you and two friends houses are located at points A, B, and C. You want to find a meet up spot that is equidistant from all three of your houses...how could you do this?

Multiple Choice

If $$\overline{AD}$$ is the perpendicular bisector of  $$\overline{AD}$$  . Find BC. 

• 6.5

• 17

• 34

• We cannot know

Angle Bisectors in triangles

• bisects one angle of a triangle

• any point on the angle bisector equidistant from two sides of the triangle (measuring perpendicularly)

Multiple Choice

All three angle bisectors of a triangle

• intersect at a point that is equidistant from the sides

• intersect at a point that is equidistant from the midpoints

• intersect at a point outside the triangle

• do not intersect at a single point

Multiple Choice

The point where the angle bisectors intersect (point G) is called the.....

• circumcenter

• incenter

• centroid

• origin

• midcenter

The Incenter

• the point where the angle bisectors intersect

• is equidistant from each SIDE (measuring perpendicularly)

• the center of the biggest circle that can be drawn inside the circle

• is always INSIDE the circle

Multiple Choice

In the triangle, point I is the incenter. If  $$m\angle CAB=64\degree$$ and  $$m\angle AIB=122\degree$$ , then find the  $$m\angle ABC$$  

• $$32\degree$$  

• $$56\degree$$  

• $$52\degree$$  

• $$26\degree$$