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In this lesson, we will learn how to use the properties of parallelograms to solve problems.

Q1:

In the figure below, given that π΄ π΅ πΆ π· is a parallelogram, determine π β π» π· πΆ .

Q2:

Q3:

In the parallelogram πΈ πΉ πΊ π» , π β πΈ π» πΊ = ( 3 π₯ + 1 9 ) β , π β π» πΊ πΉ = ( 2 π₯ + 6 ) β , and π β πΉ πΈ π» = ( 2 π¦ ) β . Find the values of π₯ and π¦ .

Q4:

Which of the following statements must be true about a parallelogram?

Q5:

How many altitudes are there in a parallelogram?

Q6:

In the figure shown, π β π· π΄ πΆ = 5 π₯ β , π β π΅ π΄ πΆ = 3 π₯ β , and π β π΄ π΅ πΆ = 4 π₯ β . Determine π β π΅ πΆ π· and π β π΄ π· πΆ .

Q7:

Which of the following are a base and its corresponding altitude in the given parallelogram?

Q8:

In the figure below, given that π΄ π΅ πΆ π· is a parallelogram, find π β π΄ .

Q9:

π΄ π΅ πΆ π· is a parallelogram such that π΄ ( β 3 , 4 ) , π΅ ( 0 , 4 ) , and πΆ ( β 2 , 2 ) . Determine the coordinates of vertex π· .

Q10:

Find π β πΆ π΅ π· .

Q11:

Which of the following statements is not true?

Q12:

Find π β π· .

Q13:

Is the following statement true or false? In a parallelogram, there is a pair of opposite sides that do not have to be parallel.

Q14:

Find the lengths of πΆ π· and π· π΄ .

Q15:

In the figure, π΄ π΅ πΆ π· and πΆ π΅ π» π are parallelograms. Find π β π΄ π΅ π» .

Q16:

In parallelogram π΄ π΅ πΆ π· , suppose π· π = 4 4 and π΅ π = 5 3 . How are the lengths π΄ π + π΄ π΅ and πΆ π + πΆ π· related?

Q17:

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

Q18:

In parallelogram π΄ π΅ πΆ π· , suppose π β π΄ + π β πΆ = 2 2 2 β . What is π β π΅ ?

Q19:

Determine whether this statement is true or false: All parallelograms are regular polygons.

Q20:

In the following figure is a parallelogram. What is the size of ?

Q21:

Is the following statement true or false? In a parallelogram, opposite sides are parallel and equal in length.

Q22:

π΄ π΅ πΆ π· is a parallelogram, where the coordinates of the points π΄ , π΅ , and πΆ are ( 4 , β 9 ) , ( 3 , 2 ) , and ( 5 , 5 ) , respectively. Find the coordinates of the vertex π· .

Q23:

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

Q24:

Which of the following statements correctly describes a property of the given shape?

Q25:

What is the sum of the measures of any two consecutive angles in a parallelogram?

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