Proportional Parts in Triangles and Parallel Lines Quiz

What does the Angle Bisector Theorem state about the relationship between the sides of a triangle?

• The angle bisector divides the opposite side into two equal segments.

• The angle bisector divides the opposite side into segments proportional to the other two sides.

• The angle bisector is perpendicular to the opposite side.

• The angle bisector creates two congruent triangles.

In problem 13, what is the missing length 'a' if a/30 is proportional to 21/15?

• 30

• 21

• 36

• 42

Which theorem is used to solve problem 14?

• Angle Bisector Theorem

• Triangle Proportionality Theorem

• Pythagorean Theorem

• Congruent Triangles Theorem

What is the missing length in problem 15 after subtracting 24 from 39?

• 18

• 15

• 21

• 12

In problem 16, what is the total indicated length if X is found to be 5?

• 16

• 12

• 14

• 10

How do you set up the proportion for problem 17 using the Angle Bisector Theorem?

• 21/10 = 14/(2x - 5)

• 21/14 = (2x - 5)/10

• 21/(2x - 5) = 14/10

• 21/14 = 10/(2x - 5)

What is the value of X in problem 17 after solving the proportion?

• 8

• 9

• 10

• 11

In problem 18, what is the final value of X after solving the equation 6(X - 1) = 60?

• 9

• 10

• 11

• 12

Which theorem is primarily used in problems 17 and 18?

• Angle Bisector Theorem

• Triangle Proportionality Theorem

• Congruent Triangles Theorem

• Pythagorean Theorem

What is the purpose of cross-multiplying in these problems?

• To find the area of a triangle

• To solve for unknown lengths

• To prove congruency

• To calculate angles