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In this lesson, we will learn how to prove that a quadrilateral is a square based on its sides, angles, and diagonals.

Q1:

Can a rhombus be a square?

Q2:

A quadrilateral has vertices at the points ( 2 , 1 ) , ( 3 , 3 ) , ( 5 , 2 ) , and ( 4 , 0 ) . By determining the lengths of the quadrilateral’s sides, and considering the gradients of the intersecting lines, what is the name of the quadrilateral?

Q3:

Name the polygon that can be graphed in the coordinate plane with vertices at ( − 2 , 3 ) , ( 3 , 3 ) , ( 3 , − 1 ) , and ( − 2 , − 1 ) .

Q4:

Is this quadrilateral a square?

Q5:

A quadrilateral has vertices at the points and . By determining the lengths of the quadrilateral’s sides, and considering the gradient of the intersecting lines, what is the name of the quadrilateral?

Q6:

Determine whether the following statement is sometimes, always, or never true: A square is a rhombus.

Q7:

Determine whether this statement is true or false: All rectangles are squares.

Q8:

Q9:

In which quadrilateral are the diagonals perpendicular and equal in length?

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