Exploring Angle and Perpendicular Bisectors in Triangles

What is an angle bisector?

• A line segment that cuts an angle into two equal parts

• A line segment that cuts a segment into two equal parts

• A line segment that forms a 90-degree angle

• A line segment that connects the midpoints of two sides

If BD is an angle bisector of triangle ABC, which angles are congruent?

• Angle ABD and Angle DBC

• Angle ABC and Angle BAC

• Angle ABD and Angle ACB

• Angle DBC and Angle BAC

What is the point called where all three angle bisectors of a triangle intersect?

• Circumcenter

• Orthocenter

• Centroid

• Incenter

What does a perpendicular bisector do?

• Cuts an angle into two equal parts

• Forms a 45-degree angle with a side

• Cuts a segment into two equal parts and forms a 90-degree angle

• Connects the midpoints of two sides

If M is the midpoint of segment ST, what can be said about SM and MT?

• SM is equal to MT

• SM is unrelated to MT

• SM is half the length of MT

• SM is twice the length of MT

What is the point called where all three perpendicular bisectors of a triangle intersect?

• Orthocenter

• Incenter

• Circumcenter

• Centroid

In a triangle, where can the circumcenter be located?

• On one of the sides of the triangle

• Either inside or outside the triangle

• Always outside the triangle

• Always inside the triangle

If KM is an angle bisector and angle 1 is 6x - 10 and angle 2 is 4x + 12, what is the value of x?

• 13

• 10

• 12

• 11

If BD is 2x + 4 and x = 12, what is the length of BD?

• 26

• 30

• 24

• 28

If BD and DC are both 28, what is the length of BC?

• 56

• 112

• 28

• 84