Geometry -Solve the missing length using the triangle bisector theorem

The video tutorial explains the concept of an angle bisector in a triangle, which divides the triangle into two similar triangles. It demonstrates how to set up proportions using the sides of the triangle and solve for unknown values using cross multiplication. The tutorial concludes with a practical example to reinforce the learning.

What does an angle bisector do in a triangle?

• It bisects the opposite side of the triangle.

• It divides the triangle into two congruent triangles.

• It cuts the angle into two equal parts, forming similar triangles.

• It divides the triangle into two equal areas.

In the given example, if the whole length is 12 and one part is 4, what is the length of the other part?

• 48

• 6

• 8

• 4

How do you set up a proportion using the bisector theorem?

• By equating the sum of the sides to the bisector.

• By comparing the lengths of the bisected angles.

• By setting the ratio of the two segments created by the bisector equal to the ratio of the other two sides.

• By dividing the triangle into two equal areas.

What is the result of cross-multiplying the proportion 5.5/X = 4/8?

• X = 44

• X = 11

• X = 22

• X = 5.5

What is the final value of X in the example provided?

• 11

• 4

• 8

• 5.5