Exploring the Segment Addition Postulate

This video tutorial covers the segment addition postulate, explaining that if a point lies between two endpoints on a line segment, the sum of the two smaller segments equals the entire segment. The tutorial includes three examples: a simple calculation, an algebraic expression, and a quadratic equation, demonstrating how to apply the postulate in different scenarios.

What does the Segment Addition Postulate state?

• If you have a line segment AB and a point B between AC, then AB + BC = AC.

• If you have a line segment AB and a point C between AB, then AC + BC = AB.

• If you have a line segment AC and a point B between AB, then AB + AC = BC.

• If you have a line segment AB and a point C between AC, then AB + AC = BC.

In the first example, if AB = 19 and AC = 31, what is the length of BC?

• 12

• 13

• 15

• 14

What is the value of X in the second example where AB = 7X + 3, BC = 3X + 13, and AC = 56?

• 3

• 2

• 5

• 4

In the second example, what is the length of AB when X = 4?

• 28

• 31

• 29

• 30

In the second example, what is the length of BC when X = 4?

• 26

• 25

• 24

• 27

In the third example, what is the quadratic equation formed when AB = X^2 + 7X, BC = 3X + 2, and AC = 26?

• X^2 + 7X + 3X + 2 = 26

• X^2 + 10X - 24 = 0

• X^2 + 7X + 3X + 2 = 0

• X^2 + 10X + 2 = 26

What are the possible values of X in the third example?

• 12 or 2

• -12 or 2

• -12 or -2

• 12 or -2

In the third example, what is the length of AB when X = 2?

• 18

• 19

• 17

• 16

In the third example, what is the length of BC when X = 2?

• 6

• 7

• 8

• 9

What is the final verification step in the third example?

• Dividing AC by AB to find BC

• Multiplying AB and BC to check if it equals AC

• Subtracting AB from AC to find BC

• Adding AB and BC to check if it equals AC