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In this lesson, we will learn how to correlate between the diagonals of parallelograms and how to use these properties to find unknown measures.

Q1:

Find the value of π§ in the following parallelogram.

Q2:

Q3:

In parallelogram π΄ π΅ πΆ π· , π΅ πΆ = 8 9 , π π΅ = 4 6 , and π πΆ = 7 8 . What is the perimeter of β³ π΄ π π· ?

Q4:

In parallelogram π΄ π΅ πΆ π· , π΅ πΆ = 4 7 , π π΅ = 4 3 , and π πΆ = 3 3 . What is the perimeter of β³ π΄ π π· ?

Q5:

If π π π π is a parallelogram, find the value of π§ .

Q6:

Q7:

π΄ π΅ πΆ π· is a parallelogram where the coordinates of π΄ are ( 7 , 7 ) and the coordinates of πΆ are ( β 1 , 5 ) . Find the coordinates of the point of intersection of the two diagonals of π΄ π΅ πΆ π· .

Q8:

π΄ π΅ πΆ π· is a parallelogram where the coordinates of π΄ are ( 7 , 5 ) and the coordinates of πΆ are ( β 1 , 3 ) . Find the coordinates of the point of intersection of the two diagonals of π΄ π΅ πΆ π· .

Q9:

What can you say about the diagonals of a parallelogram?

Q10:

In parallelogram π΄ π΅ πΆ π· , the coordinates of π΄ are ( 1 , 3 ) and those of the intersection of the diagonals are ( 4 , β 3 ) . What are the coordinates of point πΆ ?

Q11:

Given that π΄ π΅ πΆ π· is a parallelogram and πΆ π = 8 . 6 c m , find the perimeter of β³ π΄ π΅ πΆ .

Q12:

Given that π΄ π΅ πΆ π· is a parallelogram and πΆ π = 5 . 8 c m , find the perimeter of β³ π΄ π΅ πΆ .

Q13:

In a parallelogram π΄ π΅ πΆ π· , the coordinates of π΄ , π΅ , and πΆ are ( 9 , 0 ) , ( 1 1 , 0 ) , and ( β 4 , 9 ) , respectively. Find the coordinates of the point at which the two diagonals intersect, and then determine the coordinates of point π· .

Q14:

In a parallelogram π΄ π΅ πΆ π· , the coordinates of π΄ , π΅ , and πΆ are ( β 8 , 5 ) , ( 6 , 5 ) , and ( 1 3 , 8 ) , respectively. Find the coordinates of the point at which the two diagonals intersect, and then determine the coordinates of point π· .

Q15:

Given that πΆ π = 1 6 c m , determine the length of π΄ πΆ .

Q16:

The given figure shows a parallelogram π΄ π΅ πΆ π· .

Using what you know about alternate angles, determine which angle will have the same measure as β π΄ π΅ π· .

Which angle will be equal in measure to β π΄ π· π΅ ?

π΅ π· is a common side to both triangles. Using the information from the earlier parts of the question, can we prove that triangles π΄ π΅ π· and πΆ π· π΅ are congruent? If yes, by which congruence criteria?

What will be true of π΄ π΅ and πΆ π· and of π΅ πΆ and π΄ π· ?

What will be true of angles β π΅ π΄ π· and β π΅ πΆ π· and of angles β π΄ π΅ πΆ and β π΄ π· πΆ ?

Q17:

Is any quadrilateral whose diagonals bisect each other a parallelogram?

Q18:

Are the two diagonals of a parallelogram perpendicular?

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