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In this lesson, we will learn how to find a missing length in a triangle using two or three parallel lines in it using proportionality.

Q1:

Given that π΄ πΈ πΉ π· is a parallelogram, where πΈ and πΉ are the midpoints of π· π΅ and π· πΆ respectively, find the length of πΆ π΅ .

Q2:

Given that π΄ π΅ πΆ π· is a parallelogram, find π β π΅ π΄ πΈ .

Q3:

Find the length of πΆ π΅ .

Q4:

Q5:

If the perimeter of β³ π΄ π΅ πΆ = 9 . 7 c m , πΈ is the midpoint of π΄ πΆ , and π· πΈ β«½ π΅ πΆ , find the length of π· πΈ .

Q6:

On the figure, π΄ π΅ πΆ π· is a parallelogram whose diagonals intersect at π , and π is a point on π΄ π· . If π π = 3 8 , what is πΆ π· ?

Q7:

Given that π΄ π΅ πΆ π· is a parallelogram, find the length of π· π» .

Q8:

πΉ π· πΈ πΆ is a parallelogram, where πΉ and π· are the midpoints of π΄ π΅ and π΄ πΆ , respectively, and πΆ πΈ = 6 c m . Determine the length of π΅ πΆ .

Q9:

Given that the area of the parallelogram π΄ π΅ πΆ π· = 1 7 4 3 c m 2 and that of the β³ π΄ πΉ π· = 2 6 8 c m 2 , find the area of πΉ π΅ πΆ πΏ and that of the β³ πΏ πΆ πΉ .

Q10:

In the figure, π΄ π΅ πΆ π· is a parallelogram with πΉ on π΅ πΆ and rays ο« π· πΉ and ο« π΄ π΅ meeting at πΈ . Find the length of π΅ πΈ .

Q11:

In the given parallelogram, π· πΈ = 2 πΈ π and π΄ π· = 1 3 c m . Determine πΉ π· .

Q12:

Given that π is the midpoint of π· πΆ , the perimeter of β³ π΄ π· πΆ is 33 cm, π΄ π· = 7 c m , and π πΆ = 5 c m , find the length of π΄ π .

Q13:

Determine , if .

Q14:

Q15:

Given that π΄ π΅ πΆ π· is a parallelogram, find the length of π π .

Q16:

If , , and , find the length of .

Q17:

Q18:

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

Q19:

In the figure, π· π and πΈ π are parallel to π΄ πΆ and π΄ π΅ respectively. If π΅ πΆ = 1 2 c m , π΄ π· π· π΅ = 2 , and πΈ πΆ = 1 3 π΄ πΈ , determine the length of π π .

Q20:

In the figure, π· π and πΈ π are parallel to π΄ πΆ and π΄ π΅ respectively. If π΅ πΆ = 1 6 c m , π΄ π· π· π΅ = 7 9 , and πΈ πΆ = 1 3 π΄ πΈ , determine the length of π π .

Q21:

π΄ π΅ πΆ π· is a parallelogram, and π is an interior point in it, where ο« π· π bisects angle π΄ π· πΆ , and ο« πΆ π bisects angle π· πΆ π΅ . If π is the midpoint of π· πΆ and π π = 4 5 c m , determine the length of π πΆ .

Q22:

Given that π΄ π΅ πΆ π· is a parallelogram, and π β πΆ π· πΈ = 4 0 β , determine π β π΄ .

Q23:

In the figure, segments π π and π΅ πΆ are parallel. If π΄ π = 1 8 , π π΅ = 2 4 , and π΄ π = 2 7 , what is the length of π πΆ ?

Q24:

In the figure, segments π π and π΅ πΆ are parallel. If π΄ π = 3 0 , π π΅ = 1 8 , and π΄ π = 2 0 , what is the length of π πΆ ?

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