Exploring the Triangle Angle Bisector Theorem

This video tutorial explores the concept of angle bisectors in triangles, demonstrating how they divide the opposite side into two segments that are proportional to the other two sides of the triangle. The video includes a detailed example problem, illustrating the application of these properties to solve for unknown segment lengths using algebraic methods.

What is the primary focus of the video?

• Studying the Pythagorean theorem

• Exploring the angle bisector of a triangle

• Learning about congruent angles

• Understanding the properties of triangles

What does the angle bisector of a triangle do to the segments within the triangle?

• It bisects the opposite side

• It divides them into two proportional segments

• It makes them equal in length

• It creates right angles

In the angle bisector theorem, what is the relationship between the segments created?

• They are congruent

• They are proportional

• They form a right angle

• They are equal in length

What is the significance of the point where the angle bisector intersects the opposite side?

• It is the midpoint of the side

• It divides the side into two equal segments

• It creates two proportional segments

• It forms a right angle with the side

In the example, what is the proportion set up for the segments on one side of the angle bisector?

• x over 6

• x over 14

• 6 over x

• 14 over x

What is the length of the entire segment in the example problem?

• 14

• 6

• 18

• x

What equation is formed after cross-multiplying the proportions in the example?

• 14x = 6

• 6(18 - x) = 14x

• 6x = 14

• x = 18 - 6

What is the value of x after solving the equation?

• 14

• 5.4

• 6

• 18

What is the final step in solving for x in the example?

• Subtracting 6 from both sides

• Adding 6 to both sides

• Multiplying both sides by 20

• Dividing both sides by 20

Why does the value of 5.4 make sense in the context of the example?

• It is greater than 14

• It is proportional to the other segments

• It is less than 6

• It is the midpoint of the segment