Chapter Test
Sign In
Write the definition of a square. Then, recall all the theorems you've learned in the chapter and pick the ones that are relevant.
See solution.
By definition, a square is a parallelogram with four congruent sides and four right angles. That is, it is both a rhombus and a rectangle simultaneously.
Therefore, to prove that a quadrilateral is a square, first we need to prove that it is a parallelogram, then prove that it is a rhombus, and finally prove that it is a rectangle.
If any of the questions in the diagram above has Yes
as the answer, then the quadrilateral ABCD is a parallelogram.
To prove that a parallelogram is a rhombus, we must check one of the two conditions below.
Yes, then the parallelogram is a rhombus.
Finally, to prove that a parallelogram is a rectangle, we must verify either that it has four right angles or that its diagonals are congruent. Let's review the Rectangle Diagonals Theorem.
|
Rectangle Diagonals Theorem |
|
A parallelogram is a rectangle if and only if its diagonals are congruent. |