Transcript Rectangles

Rectangles
Rectangle - A parallelogram with four right
angles.
Theorem 8.13
• If a parallelogram is a rectangle, then its
diagonals are congruent.
Theorem 8.14
• If the diagonals of a parallelogram are
congruent, then it is a rectangle.
Rectangles
Summary of Properties of a Rectangle:
• Opposite sides are parallel.
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other.
• All four angles are right angles.
• Diagonals are congruent.
Quadrilateral EFGH is a rectangle. If
find x.
Answer: 5
and
Quadrilateral EFGH is a rectangle.
a. Find x.
b. Find y.
Answer: 7
Answer: 11
Max is building a swimming
pool in his backyard. He
measures the length and
width of the pool so that
opposite sides are parallel. He
also measures the diagonals
of the pool to make sure that
they are congruent. How does
he know that the measure of
each corner is 90?
Answer: Since opposite sides are parallel, we know that
RSTU is a parallelogram. We know that
.
A parallelogram with congruent diagonals is a
rectangle. Therefore, the corners are
Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3),
Y(3, 1), and Z(2, –1). Determine whether WXYZ is a
rectangle using the Distance Formula.