# Worksheet: Applications of Parallel Lines in a Triangle

In this worksheet, we will practice finding a missing length in a triangle using two or three parallel lines in it using proportionality.

**Q1: **

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

**Q2: **

Determine , if .

- A
- B
- C
- D

**Q3: **

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

**Q4: **

Find the length of .

**Q5: **

If , , and , find the length of .

**Q6: **

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

**Q7: **

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

**Q9: **

Given that is a parallelogram, find .

**Q10: **

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

**Q11: **

Given that is a parallelogram, find the length of .

**Q12: **

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

**Q13: **

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

**Q14: **

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

**Q15: **

In the given parallelogram, and . Determine .

**Q16: **

Given that is a parallelogram, 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: **

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 .

**Q20: **

Given that is a parallelogram, and , determine .

**Q21: **

Given that is a rectangle, and is a parallelogram, find the area of .

**Q22: **

Given that , , and , find .

**Q23: **

Find the length of .

**Q24: **

Determine , if .

- A
- B
- C
- D