Angle Bisectors and Segment Lengths

This video tutorial covers solving for unknown values using the properties of angle bisectors. It begins by explaining that a ray bisecting an angle creates two congruent angles. The tutorial then provides two examples: the first involves setting up and solving an equation for x when given congruent angles, and the second uses congruent segments to solve for x. The video concludes by verifying the congruence of segments and calculating their lengths.

What does it mean when a ray bisects an angle?

• The ray creates an obtuse angle.

• The ray creates a right angle.

• The ray divides the angle into three equal parts.

• The ray divides the angle into two equal parts.

If angle BAD measures 32 degrees, what is the measure of angle DAF?

• 16 degrees

• 48 degrees

• 32 degrees

• 64 degrees

How do you solve the equation 3x - 1 = 32 for x?

• Subtract 1 from both sides, then divide by 3.

• Divide both sides by 3, then subtract 1.

• Multiply both sides by 3, then add 1.

• Add 1 to both sides, then divide by 3.

What is the value of x if 3x + 15 equals 5x - 12?

• x = 15

• x = 11

• x = 10

• x = 13.5

What property of angle bisectors is used to determine that two segments are congruent?

• The segments are equal in length.

• The segments are parallel.

• The segments are perpendicular.

• The segments are equidistant from the angle sides.

What is the final step in solving for x in the equation 3x + 15 = 5x - 12?

• Divide both sides by 2.

• Add 12 to both sides.

• Subtract 15 from both sides.

• Subtract 5x from both sides.

How do you calculate the length of a segment using x = 13.5 in the expression 3x + 15?

• Multiply 13.5 by 3, then subtract 15.

• Multiply 13.5 by 3, then add 15.

• Add 15 to 13.5, then multiply by 3.

• Subtract 15 from 13.5, then multiply by 3.

What is the length of the segment when x = 13.5 in the expression 5x - 12?

• 67.5

• 55.5

• 40.5

• 27.5

Why is it important to verify the length of segments in angle bisector problems?

• To check if the segments are perpendicular.

• To determine if the segments are equal in area.

• To ensure the segments are parallel.

• To confirm the segments are congruent.

What is the significance of the examples covered in the video?

• They demonstrate how to create angles.

• They show how to solve for unknowns using angle bisectors.

• They illustrate how to measure angles.

• They explain how to draw bisectors.