# Worksheet: Angle Bisector Theorem and Its Converse

In this worksheet, we will practice using the theorem of angle bisector and its converse to find a missing side length in a triangle.

Q1:

In the given figure, , , and . If , what is the value of ? Q2:

In the figure, bisects , , , and the perimeter of is 57. Determine the lengths of and . • A,
• B,
• C,
• D,

Q3:

Given that angle is bisected by , , , and . Determine the lengths and . • A,
• B,
• C,
• D,

Q4:

If , , and , find the ratio between the areas of the and the . • A
• B
• C
• D

Q5:

Find the lengths of and in the figure. • A,
• B,
• C,
• D,

Q6:

If is a right triangle at , , , and , calculate the value of . Q7:

If is a quadrilateral in which , , , , where bisects and intersects at , find the value of the ratio .

• A
• B
• C
• D

Q8:

Given that is a triangle in which , find the value of each of and . • A,
• B,
• C,
• D,

Q9:

In the triangle , , , and . Given that bisects and intersects at , determine the length of . Q10:

Given that in the figure, , , and , what is ? Q11:

If and , determine the perimeter of . Q12:

Using the figure below, find the length of to the nearest hundredth. Q13:

In triangle , lies on such that bisects . Given , , and , determine to the nearest hundredth.

Q14:

Use the figure to determine length to two decimal places. Q15:

Given that , , and , what is ? Q16:

is a right-angled triangle at , where bisects and intersects at . Given that , , determine the perimeter of .

Q17:

In the given figure, if , find . • A
• B
• C
• D

Q18:

If and , find . Leave your answer as a fraction in its simplest form. • A
• B
• C
• D

Q19:

Suppose that in the figure, . What is ? Q20:

is a chord in a circle. major arc such that . is the midpoint of the minor arc . is drawn to intersect at . Determine the ratio between the areas of and .

• A4
• B
• C2
• D1

Q21:

is a triangle in which , , and . , where , and intersects at . If bisects , find the length of . Q22:

Given that , , , and , find the numerical value of . Q23:

In the shown figure, determine . • A
• B
• C
• D

Q24:

is a triangle, where is the midpoint of , and . If the bisector of intersects at , find the value of .

• A
• B
• C
• D

Q25:

In the figure, . What is ? • A
• B
• C
• D