Angle Bisector Theorem Concepts

This video tutorial explains the angle bisector proportions theorem, which states that if a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the adjacent sides. The video provides an example using a triangle with an angle bisector, demonstrating how to set up and solve proportions to find unknown segment lengths. The tutorial emphasizes the concept of matching left and right sides of the triangle to set up the correct proportion, and it includes a step-by-step solution to find the length of a segment labeled as 'X'.

What does the angle bisector proportions theorem state?

• A ray bisecting an angle of a triangle divides the opposite side into two equal parts.

• A ray bisecting an angle of a triangle has no effect on the opposite side.

• A ray bisecting an angle of a triangle creates two congruent triangles.

• A ray bisecting an angle of a triangle divides the opposite side proportionally to the adjacent sides.

In the given example, what is the relationship between segments AB, BD, AC, and CD?

• AB/CD = AC/BD

• AB/BD = CD/AC

• AB/AC = BD/CD

• AB/BD = AC/CD

What is the purpose of using a memory device in the example?

• To identify the triangle's type

• To recall the theorem's name

• To easily set up the proportion between segments

• To remember the names of the segments

In the basic example, which angles are congruent?

• Angle R and angle S

• Angle R and angle SVT

• Angle R and angle V

• Angle R and angle T

What is the unknown segment labeled as in the basic example?

• W

• X

• Z

• Y

Why does the teacher bar the letter 'S' in the example?

• To make it look like a number

• To distinguish it from the number 5

• To make it look like a pie

• To emphasize its importance

What is the first step in solving the example problem?

• Cross-multiply the segments

• Find the congruent angles

• Set up the proportion

• Simplify the equation

What is the proportion set up in the example problem?

• 8/4 = 10/X

• 8/X = 4/10

• 10/8 = X/4

• X/8 = 4/10

What operation is performed after setting up the proportion?

• Cross-multiplication

• Addition

• Division

• Subtraction

What is the value of X in the example problem?

• 7

• 4

• 5

• 6