Quadrilaterals Worksheet With Answers Page 40
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50To prove a parallelogram is a square, one of the following theorems can be used.
Theorems
1. If the diagonals of a parallelogram are
congruent and perpendicular, then the
parallelogram is a square.
2. If the parallelogram has one right angle and
two adjacent sides congruent, then the
parallelogram is a square.
These theorems are converses of previously stated theorems for squares.
Theorem: If a parallelogram is a square, then its diagonals are congruent and
perpendicular.
Converse: If the diagonals of a parallelogram are congruent and perpendicular, then the
parallelogram is a square.
Theorem: If a parallelogram is a square, then the parallelogram has one right angle and
two adjacent sides congruent.
Converse: If a parallelogram has one right angle and two adjacent sides congruent, then
the parallelogram is a square.
We will apply the properties of squares and rhombi in the following examples.
Examples
1. Given: Square ABCD with diagonals DB and AC
Find:
x , y , and the indicated measures
D
C
M
A
B
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