Page 25 - Math Course 3 (Book 2)

Properties of Rectangles

Angles of a Rectangle
Quadrilateral EFGH is a rectangle. Find x. MO. 7 - L4b

A. 6 Parallelograms as Rectangles
B. 7
C. 9
D. 14
Let’s Begin
F G
(4y – 5)°

(x² + 2)° Rectangle on a Coordinate Plane
(14x – 47)°

E H Example

Quadrilateral ABCD has vertices A(–2, 1), B(4, 3),
C(5, 0), and D(–1, –2). Determine whether ABCD is
Answer
a rectangle using the Slope Formula.
Method 1: Y – y
1
2
Use the Slope Formula, , to see if
m =
x – x
1
2
opposite sides are parallel and consecutive sides
are perpendicular.
Diagonals of a Parallelogram
Max is building a swimming pool in his backyard.
He measures the length and width of the pool so B(4, 3)
that opposite sides are parallel. He also measures
the diagonals of the pool to make sure that they are A(–2, 1)
congruent. How does he know that the measure of
each corner is 90? D(5, 0)
S T

D(–1, –2)

3 – 1 1
Slope of AB = or
4 – (–2) 3
–2 – 0 1
Slope of CD = or – 3
–1 – 5
0 – 3
Slope of BC = or –3
R U 5 – 4
1 – (–2)
Slope of AD = or –3
A. Since opp. sides are ||, STUR must be a –2 – (–1)
rectangle. Because AB||CD and BC||AD quadrilateral ABCD is
B. Since opp. sides are ≅, STUR must be a
rectangle. a parallelogram. The product of the slopes of
C. Since diagonals of the ▱ are ≅, STUR must consecutive sides is –1. This means that AB ▱ BC
be a rectangle. , AB ▱ AD, AD ▱ CD, and BC ▱ CD.
D. STUR is not a rectangle.
The perpendicular segments create
Answer four right angles. Therefore, by
Answer definition ABCD is a rectangle.

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