Relationships Within Triangles

Relationships Within Triangles

Perpendicular Bisector Theorem

• In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

  
  

• If  $\overline{CP}$  is the  $\perp$  Bisector of  $\overline{AB}$  then AC=CB and a right angle is formed where the the two lines meet 

Multiple Choice

A line that is perpendicular to a segment at its midpoint is called a ____________.

• midsegment

• perpendicular bisector

• median

• altitude

Multiple Choice

A point is ________ from two figures if the point is the same distance from each figure.

• equidistant

• concurrent

• perpendicular

• bisected

Multiple Choice

Find the value of x.

• 2

• 6

• 8

• 4

Multiple Choice

Find the value of x.

• 8

• 16

• 4

• 32

Multiple Choice

What is UT?

• A line segment

• 3

• 15

Multiple Choice

 In the isosceles triangle  $QRS$  ,  $\overline{RT}$  is the angle bisector of  $\angle QRS$ . You want to prove the base angles of this triangle are congruent. You start by stating  $\angle1\cong\angle2$  . What is a valid reason for this statement? 

• Reflexive property of congruence

• Definition of angle bisector

• Symmetric property of congruence

• Corresponding angles are congruent

Multiple Choice

Given  $AM=BM$   and  $AC=BC$  , what is $m\angle MBC$  ?

• 26

• 90

• 64

• 13

Multiple Choice

• Perpendicular Bisector
• Angle Bisector
• Median
• Midsegment

Multiple Choice

What goes from the vertex, bisects the angle at that vertex, and connects to the opposite side?

• Angle Bisector
• Perpendicular Bisector
• Median
• Midsegment