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In this lesson, we will learn how to use parallelism of lines to find a missing length of a line segment in a transversal line cut by parallel lines.

Q1:

Using the information in the figure, determine the length of πΈ πΉ .

Q2:

Given that π΄ πΆ = 7 . 5 c m , π΅ π· = 1 4 c m , πΉ π = 2 5 . 2 c m , and πΉ πΎ = 4 2 c m , determine the lengths of πΆ π and π· πΉ .

Q3:

If πΆ πΈ = ( π₯ + 2 ) c m , what is π₯ ?

Q4:

In the given figure, find the values of π₯ and π¦ .

Q5:

Given that π΄ π· = π₯ c m , π· π΅ = 3 0 c m , π΅ πΈ = ( π₯ + 7 ) c m , and πΈ πΆ = 1 8 c m , find the value of π₯ .

Q6:

In the figure, lines πΏ , πΏ , πΏ ο§ ο¨ ο© , and πΏ οͺ are all parallel. Given that π π = 1 2 , π π = 8 , π΄ π΅ = 1 0 , and π΅ πΆ = 5 , what is the length of πΆ π· ?

Q7:

Find the lengths of πΈ πΆ and π· π΅ .

Q8:

Given that π΄ π΅ = 2 4 c m , π΄ π· = 3 6 c m , π΄ πΆ = 1 8 c m , and πΈ π = 1 5 c m , find the length of π΄ πΈ and π· π .

Q9:

Given the following figure, find the numerical values of π₯ and π¦ .

Q10:

In the figure, π΄ π΅ = 3 π₯ , π΅ πΆ = 5 π₯ , π· πΈ = ( 3 π₯ β 6 ) , and πΈ πΉ = ( 4 π₯ β 3 ) . Find the value of π₯ .

Q11:

In the following figure, π΄ π΅ = ( 5 π₯ + 4 ) c m , π΅ πΆ = ( 6 π₯ β 4 ) c m , π· πΈ = ( 4 π₯ β 3 ) c m , and πΈ πΉ = ( 4 π¦ β 7 ) c m . Find the values of π₯ and π¦ .

Q12:

Given that π΄ π΅ = ( 2 π₯ + 4 ) cm, π· πΊ = ( 3 π₯ + 2 ) cm, π΄ πΆ = ( 2 π¦ + 2 ) cm, π΄ πΊ = 4 c m , and π΄ πΉ = 5 c m , find the lengths of π΄ πΈ and π· πΊ .

Q13:

Find the values of π₯ and π¦ .

Q14:

Given that π΄ π΅ = ( 2 π₯ + 1 ) cm, π΅ πΆ = ( π₯ + 3 ) cm, π· πΈ = ( 3 π₯ β 1 ) cm, πΈ πΉ = π¦ c m , πΊ π» = 1 1 c m , and π» πΌ = 1 0 c m , find the values of π₯ and π¦ .

Q15:

Given that , , and , determine the values of and .

Q16:

In the diagram below, π΄ π΅ = 1 0 , π΅ πΆ = ( π₯ + 1 ) , πΆ π· = 2 0 , πΈ πΉ = 1 0 , and πΉ πΊ = 1 0 . Find the value of π₯ and the length of πΊ π» .

Q17:

In the figure, given that π΅ πΆ = 9 4 , what is π΅ πΈ ?

Q18:

Suppose π π and π πΏ intersect at point π , and that π π and πΏ π are parallel. If π π = 4 6 , π π = 6 4 , and π πΏ = 1 6 5 , what is π π ?

Q19:

Suppose that, in the figure, π΄ πΆ = 3 0 and π β πΈ π· π΅ = 1 3 9 β . What is the length of π΄ πΈ ?

Q20:

Given that π πΏ = 2 3 4 c m , find the length of π π .

Q21:

Given that πΈ π· β₯ πΆ π΅ , find the value of π₯ .

Q22:

Draw β³ π΄ π΅ πΆ with π΄ π΅ = 8 , π β π΄ = 3 9 β , and π β π΅ = 6 8 β . Bisect π΄ πΆ at π· , and draw β ο© ο© ο© ο© β π· πΈ parallel to π΄ π΅ and meeting π΅ πΆ at πΈ . Find the lengths π΅ πΈ , πΆ πΈ , and π· πΈ rounded to one decimal place.

Q23:

Given that π΄ π = 1 6 c m , π· π = 2 1 c m , and π΄ π΅ = 8 8 . 5 3 c m , find the perimeter of β³ π΄ π· π . Round your answer to two decimal places.

Q24:

π , π , and π are three parallel planes intersected by the two coplanar straight lines πΏ ο§ and πΏ ο¨ . If π΄ π΅ π΅ πΆ = 2 3 , π΄ π· = 1 5 c m , and πΆ πΉ = 1 3 c m , find the length of π΅ πΈ .

Q25:

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