6.1 Perp. & Angle Bisectors and 6.2 Bisectors of Triangles

6.1 Perp. & Angle Bisectors and 6.2 Bisectors of Triangles

by Mary Lett

​Objective and Standards

• ​Students will be able to identify perpendicular bisectors, angle bisectors, circumcenter, and incenter of a triangle and the relationships formed by these objects.

​Colorado Standards:

​HSG-CO.C.9, HSG-MG.A.1, HSG-CO.C.10, HSG-CO.D.12, HSG-C.A.3, HSG-MG.A.3

​Vocabulary

​Find each measure.

Multiple Choice

Can you use the Perpendicular Bisector Theorem on this image?

• Yes

• No

Multiple Choice

Find the measure of Angle NJZ

• 50 degrees
• 40 degrees
• 38 degrees
• 76 degrees

Multiple Choice

Find HG

• 28
• 14
• 41
• 7

Fill in the Blanks

Suppose line m is the perpendicular bisector of  $\overline{AB}$  . Find the value of x. 

Fill in the Blanks

In the diagram,

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

Fill in the Blanks

Find the value of x.

​Vocabulary

​Vocabulary

​Vocabulary

Multiple Choice

Define: INCENTER OF A TRIANGLE

• the intersection point of the three angle bisectors of a triangle 
• when three or more lines intersect at a single point 
• the intersection point of the three perpendicular bisectors of a triangle 
• the point of intersection of three or more lines 

Multiple Choice

Define: CIRCUMCENTER OF A TRAINGLE

• the intersection point of the three perpendicular bisectors of a triangle 
• when a circle passes through the three vertices of a triangle 
• the point of intersection of three or more lines 
• the intersection point of the three angle bisectors of a triangle 

Multiple Choice

Which point is equidistant from the vertices?

• Circumcenter
• Incenter
• Neither
• Bilateral

Multiple Choice

Which point is equidistant from the sides?

• Circumcenter
• Incenter
• Neither
• Bilateral

Multiple Choice

The circumcenter can be outside the triangle if the triangle is ...

• obtuse

• acute

• iscolese

• right

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

Find the value of x

• x=28
• x=14
• x=23
• x=46

Multiple Choice

G is the incenter of the triangle. What is the length of BG?

• 8

• 16

• 17

• 34