Exploring Angle Bisectors and Their Theorem

What does an angle bisector do to an angle?

• It halves the angle and then doubles it.

• It divides the angle into two equal parts.

• It triples the angle.

• It divides the angle into two unequal parts.

If a point is on the angle bisector, what can be said about its distance from the sides of the angle?

• It is equidistant from both sides.

• It is closer to one side than the other.

• It is farther from one side than the other.

• It is at an arbitrary distance from both sides.

In Example A, what is the length of the perpendicular lines from point Y to the sides of the angle?

• 6 units

• 5 units

• 8 units

• 7 units

In Example A, why is point Y on the angle bisector?

• Because it is closer to one side.

• Because it is at an arbitrary distance from both sides.

• Because the perpendicular distances from Y to the sides are equal.

• Because it is farther from one side.

In Example B, what is the equation used to find the value of x?

• 4x + 5 = 23

• 4x - 5 = 23

• 4x - 5 = 28

• 4x + 5 = 28

What is the value of x in Example B?

• 7

• 6

• 8

• 5

In Example C, what is the first step to solve for x?

• Divide by 5

• Distribute the 2

• Subtract x from both sides

• Add 7 to both sides

What is the equation after distributing the 2 in Example C?

• 3x + 4 = x + 7

• 3x - 4 = x + 7

• 6x + 8 = x + 7

• 6x - 8 = x + 7

What is the value of x in Example C?

• 5

• 4

• 3

• 2

What is the length of the sides after solving for x in Example C?

• 11 units

• 8 units

• 9 units

• 10 units