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In this lesson, we will learn how to determine if a parallelogram is a rectangle in terms of its sides, angles, and/or diagonals.

Q1:

A parallelogram π΄ π΅ πΆ π· has vertices π΄ ( β 5 , 5 ) , π΅ ( 9 , 3 ) , πΆ ( 8 , β 4 ) , and π· ( β 6 , β 2 ) .

Calculate the length of π΄ πΆ . Give an exact answer.

Calculate the length of π΅ π· . Give an exact answer.

Hence, state whether or not the parallelogram is a rectangle.

Q2:

A parallelogram has vertices at the coordinates π΄ ( β 4 , β 1 ) , π΅ ( 0 , β 3 ) , πΆ ( β 1 , β 5 ) , and π· ( β 5 , β 3 ) .

Work out the length of the diagonal π΄ πΆ .

Work out the length of the diagonal π΅ π· .

Using these lengths, is the parallelogram π΄ π΅ πΆ π· a rectangle?

Q3:

A quadrilateral has vertices at ( 0 , 3 ) , ( 1 , 5 ) , ( 5 , 3 ) , and ( 4 , 1 ) .

Decide if the quadrilateral is a parallelogram by calculating the length of each side.

Decide if the quadrilateral is a rectangle by calculating the length of its diagonals.

Q4:

A parallelogram π΄ π΅ πΆ π· has vertices at the coordinates π΄ ( β 1 , 2 ) , π΅ ( 0 , 4 ) , πΆ ( 3 , 1 ) , and π· ( 2 , β 1 ) .

Work out the slope of π΄ π΅ .

Work out the slope of π΅ πΆ .

Work out the product of the slopes from parts (a) and (b).

Is π΄ π΅ πΆ π· a rectangle?

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