Worksheet: Proving That a Quadrilateral Is a Square

In this worksheet, we will practice proving that a quadrilateral is a square based on its sides, angles, and diagonals.

Q1:

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

• A rhombus
• B rectangle
• C parallelogram
• D square
• Etrapezium

Q2:

• ANo
• BYes

Q3:

• AYes
• BNo

Q4:

Can a rhombus be a square?

• Ayes
• Bno

Q5:

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

• A never true
• B sometimes true
• C always true

Q6:

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

• Arhombus
• Brectangle
• Csquare

Q7:

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

• Afalse
• Btrue

Q8:

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?

• A rhombus
• B rectangle
• C parallelogram
• D square
• Etrapezium

Q9:

Name the polygon that can be graphed in the coordinate plane with vertices at , and .

• A Triangle
• B Rhombus
• C Square
• D Rectangle