Midpoints, Bisectors, and Angle Measures

This video tutorial covers the concepts of midpoints and angle bisectors in geometry. It explains how a midpoint divides a segment into two congruent parts and how an angle bisector divides an angle into two congruent angles. The tutorial includes problem-solving examples to illustrate these concepts, using algebraic expressions to find unknown values. It also explores advanced problems involving midpoints and segment ratios, providing a comprehensive understanding of these geometric principles.

Which point is a midpoint if it divides a segment into two equal parts?

• Point A

• Point B

• Point C

• Point D

What is a segment bisector?

• A line that divides a segment into two unequal parts

• A ray that divides an angle into two equal parts

• A line that divides a segment into two equal parts

• A point that divides a segment into two equal parts

An angle bisector divides an angle into how many congruent parts?

• Four

• One

• Two

• Three

If B is the midpoint of segment AC, and AB is 2x + 4, what is BC if BC is 5x - 8?

• 2x + 4

• 5x - 8

• 12

• 24

What is the length of segment AC if AB and BC are both 12 units?

• 24

• 36

• 48

• 12

If ray BD bisects angle ABC, and angle ABC is 11x + 5, what is the measure of angle ABD?

• 5x + 6

• 11x + 5

• 41

• 30

If the ratio of segment BC to CD is 3:7 and BC is 15 units, what is the length of segment AD?

• 150

• 100

• 65

• 50

What is the value of x if 3x equals 15?

• 3

• 5

• 7

• 10

If angle DBC is 5x + 6 and x is 7, what is the measure of angle DBC?

• 41

• 35

• 50

• 30

If AB is congruent to BD and BC is 15 units, what is the length of AD?

• 50

• 65

• 80

• 100