Exploring the Triangle Angle Bisector Theorem

This video tutorial explains the triangle angle bisector theorem, which states that an angle bisector in a triangle divides the opposite side into two segments proportional to the other two sides. The video provides multiple examples demonstrating how to apply the theorem to solve for unknown side lengths using proportions and cross multiplication. Each example builds on the previous one, increasing in complexity and requiring additional steps such as simplifying fractions and handling unknown total lengths.

What does the Triangle Angle Bisector Theorem state?

• An angle bisector in a triangle divides the triangle into two right triangles.

• An angle bisector in a triangle creates two congruent triangles.

• An angle bisector in a triangle divides the opposite side into two segments proportional to the other two sides.

• An angle bisector in a triangle divides the opposite side into two equal segments.

In Example 1, what is the value of x when 4.8/x = 12/18?

• 8.2

• 9.2

• 7.2

• 6.2

In Example 2, what is the value of x when 36/40 = x/54?

• 46.6

• 47.6

• 48.6

• 49.6

In Example 3, what is the missing side length if the total length is 39 and one side is 15?

• 22

• 24

• 25

• 23

In Example 3, what is the value of x when 15/24 = x/36?

• 22.5

• 23.5

• 21.5

• 20.5

In Example 4, what is the value of x when 12/(x-12) = 3/5?

• 33

• 30

• 31

• 32

In Example 4, what is the total length of the side if x is 32 and one segment is 12?

• 32

• 22

• 24

• 20

In Example 5, what is the value of x when 27/18 = (3x-9)/(x+11)?

• 16

• 15

• 17

• 18

In Example 5, what is the reduced form of the fraction 27/18?

• 6/5

• 5/4

• 4/3

• 3/2

In Example 5, what is the value of 3x + 33 when x = 17?

• 81

• 84

• 87

• 90