Triangle Angle Bisector Theorem Problems

This video tutorial explains the triangle angle bisector theorem, which states that a ray bisecting an angle of a triangle divides the opposite side into segments proportional to the other two sides. The video provides two examples to demonstrate how to solve for unknown values using this theorem. In the first example, the proportion is set up and solved by cross-multiplying, while the second example involves a different equation setup, also solved by cross-multiplying. The tutorial concludes with a summary of the solutions and their implications.

What does the Triangle Angle Bisector Theorem state about the segments created by a bisected angle?

• They are equal in length.

• They form a right angle.

• They are proportional to the other two sides of the triangle.

• They are perpendicular to the base.

In the first example, what is the proportion set up to solve for x?

• 15:4x+1 = 5:3

• 4x+1:5 = 3:15

• 3:5 = 15:4x+1

• 5:3 = 4x+1:15

After solving for x in the first example, what is the value of x?

• 5

• 6

• 7

• 8

What is the length of the side calculated after finding x in the first example?

• 20 units

• 22 units

• 25 units

• 28 units

In the second example, what is the initial proportion set up to solve for x?

• 3x-3:4 = 18:10

• 4:3x-3 = 10:18

• 18:10 = 3x-3:4

• 10:18 = 4:3x-3

What is the result of the cross multiplication in the second example?

• 10x - 30 = 72

• 10x + 30 = 72

• 30x - 30 = 72

• 30x + 30 = 72

What is the value of x in the second example after solving the equation?

• 3.8

• 3.6

• 3.4

• 3.2

How is the fraction 3 and 12/30 simplified in the second example?

• 3 and 4/5

• 3 and 3/5

• 3 and 2/5

• 3 and 1/5

What is the decimal equivalent of the fraction 3 and 2/5?

• 3.5

• 3.4

• 3.2

• 3.3

What is the main purpose of the video tutorial?

• To explain the Triangle Angle Bisector Theorem and solve related problems.

• To introduce the concept of congruent triangles.

• To demonstrate the Pythagorean Theorem.

• To discuss the properties of isosceles triangles.