# Worksheet: Applications of Parallel Lines in a Triangle

Q1:

Given that is a parallelogram, where and are the midpoints of and respectively, find the length of .

Q2:

Given that is a parallelogram, find .

• A
• B
• C
• D

Q3:

Find the length of .

Q4:

Find the length of .

Q5:

If the perimeter of , is the midpoint of , and , find the length of .

Q6:

On the figure, is a parallelogram whose diagonals intersect at , and is a point on . If , what is ?

Q7:

Given that is a parallelogram, find the length of .

Q8:

is a parallelogram, where and are the midpoints of and , respectively, and . Determine the length of .

Q9:

Given that the area of the parallelogram and that of the , find the area of and that of the .

• A area of , area of
• B area of , area of
• C area of , area of
• D area of , area of
• E area of , area of

Q10:

In the figure, is a parallelogram with on and rays and meeting at . Find the length of .

Q11:

In the given parallelogram, and . Determine .

Q12:

Given that is the midpoint of , the perimeter of is 33 cm, , and , find the length of .

Q13:

Determine , if .

• A
• B
• C
• D

Q14:

Determine , if .

• A
• B
• C
• D

Q15:

Given that is a parallelogram, find the length of .

Q16:

If , , and , find the length of .

Q17:

Given that is a parallelogram, find the length of .

Q18:

If the perimeter of the parallelogram below is 39.6 cm, find the length of .

Q19:

In the figure, and are parallel to and respectively. If , , and , determine the length of .

Q20:

In the figure, and are parallel to and respectively. If , , and , determine the length of .

Q21:

is a parallelogram, and is an interior point in it, where bisects angle , and bisects angle . If is the midpoint of and , determine the length of .

Q22:

Given that is a parallelogram, and , determine .

• A
• B
• C
• D

Q23:

In the figure, segments and are parallel. If , , and , what is the length of ?

Q24:

In the figure, segments and are parallel. If , , and , what is the length of ?