Solving for Missing Sides with the Angle Bisector Theorem

Mr. Allen explains how to solve for missing lengths in triangles using properties of similarity. He demonstrates setting up proportions with side lengths and solving for unknowns using cross-multiplication. The video covers two problems, highlighting the importance of congruent angles and proportionality in triangles.

What are the given dimensions of triangle ABC?

• AB = 10, AC = 14, DC = 8

• AB = 10, AC = 8, DC = 14

• AB = 14, AC = 10, DC = 8

• AB = 8, AC = 10, DC = 14

What property is used to solve for the missing length in the triangle?

• Congruent sides

• Parallel lines

• Angle bisector

• Perpendicular bisector

Which of the following is a correct proportion to solve for x?

• 10/14 = x/8

• 10/x = 8/14

• 10/8 = x/14

• 14/10 = 8/x

What is the simplified form of the proportion 10/14?

• 3/2

• 5/7

• 7/5

• 2/3

What is the value of x in the first triangle problem?

• 5.7

• 7.2

• 6.4

• 8.1

What is the total length of CB in the second triangle problem?

• 16

• 12

• 8

• 20

What is the length of CD in the second triangle problem?

• 12

• 8

• 16

• 20

What is the simplified form of the proportion 16/12?

• 2/3

• 4/3

• 3/4

• 3/2

What is the value of x in the second triangle problem?

• 10.6

• 11.3

• 9.8

• 8.5

What mathematical property is used to solve both triangle problems?

• Congruent angles

• Proportional sides

• Perpendicular bisectors

• Parallel lines