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In this lesson, we will learn how to find unknown lengths in trapezoids using the midsegment of a trapezoid theorem.

Q1:

In the figure, πΏ π» is the midsegment of trapezoid πΉ πΊ π½ πΎ . What is the value of π₯ ?

Q2:

Q3:

Q4:

In a trapezium π΄ π΅ πΆ π· where π΄ π· β«½ π΅ πΆ , the point π is the midpoint of π΄ π΅ , π is the midpoint of π· πΆ , and π π = 2 7 c m . The area of the trapezium is 513 cm^{2} and π΅ πΆ = 2 9 c m .

Find the length of π΄ π· and the perpendicular distance between π΄ π· and π΅ πΆ .

Q5:

If π΅ π΄ = 2 4 c m and π· πΆ = 2 6 c m , find the length of πΎ πΉ .

Q6:

If π΅ π΄ = 1 0 c m and π· πΆ = 1 2 c m , find the length of πΎ πΉ .

Q7:

If π΅ π΄ = 3 4 c m and π· πΆ = 2 4 c m , find the length of πΎ πΉ .

Q8:

Find the length of the middle base of a trapezium whose parallel bases are 107 cm and 246 cm.

Q9:

Find the length of the middle base of a trapezium whose parallel bases are 14 cm and 46 cm.

Q10:

Find the length of the middle base of a trapezium whose parallel bases are 27 cm and 54 cm.

Q11:

Suppose that π΄ π΅ = 1 2 8 and π π = 9 5 . What is πΆ π· ?

Q12:

Suppose that π΄ π΅ = 1 6 8 and π π = 1 4 9 . What is πΆ π· ?

Q13:

Suppose that π΄ π΅ = 1 9 6 and π π = 1 7 7 . 5 . What is πΆ π· ?

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