Exploring Angle Bisectors in Triangles

What is the primary focus of Chapter 5, Section 3?

• Perpendicular bisectors of triangles

• Median of triangles

• Angle bisectors of triangles

• Altitude of triangles

According to the Angle Bisector Theorem, if a point lies on the bisector of an angle, it is:

• At the vertex of the angle

• At the midpoint of the angle

• Closer to one side of the angle

• Equidistant from the two sides of the angle

In the Angle Bisector Theorem, what is the shortest distance between a point and the sides of an angle?

• The distance along the base

• The distance along the angle bisector

• The distance along the angle

• The perpendicular distance

If AD bisects angle BAC and DB is perpendicular to AB, what can be said about the distances from D to B and D to C?

• Cannot be determined

• They are equal

• D to C is longer

• D to B is longer

What does the converse of the Angle Bisector Theorem state?

• If a point is equidistant from the two sides of an angle, then it lies on the median

• If a point is equidistant from the two sides of an angle, then it lies on the angle bisector

• If a point is equidistant from the two sides of an angle, then it lies on the altitude

• If a point is equidistant from the two sides of an angle, then it lies on the perpendicular bisector

In Example 1, if angle CBE is 31 degrees, what can be inferred about the angle?

• It is a right angle

• It is an obtuse angle

• It is not bisected

• It is bisected

In Example 2, for what value of x does P lie on the angle bisector of angle J?

• x = 5

• x = 6

• x = 8

• x = 7

If 13x equals 11x + 8, what is the value of x?

• x = 2

• x = 8

• x = 4

• x = 6

In Example 5, what additional information is needed to conclude that AC bisects angle DA?

• The lengths of the two pieces

• The lengths of AC and DA

• The lengths of the two sides

• The angles being right angles

What is the key concept discussed in this section?

• Altitude theorem

• Angle bisector theorem and its converse

• Perpendicular bisector theorem

• Median theorem