Page 31 - Math Course 3 (Book 2)

Properties of Squares and Rhombi

MO. 7 - L5b

Properties of Squares

Explore
Plot the vertices on a coordinate plane.
Vocabulary A-Z Plan

Let us learn some vocabulary If the diagonals are perpendicular, then ABCD is
either a rhombus or a square. The diagonals of a
rectangle are congruent. If the diagonals are con-
square gruent and perpendicular, then ABCD is a square.
A quadrilateral that has equal sides and every
angle is a right angle (90°). Also opposite sides are Solve
parallel. Use the Distance Formula to compare the lengths
of the diagonals.
A square also fits the definition of a rectangle
(all angle are 90), and a rhombus (all sides are BD = 2 2
equal length) (–1–2) + [3 –( –2)]
Squares = 9 + 25
Rhombi Rectangles
= 34

AC = [3–(–2)] + [2 –( –1)] 2
2
= 25 + 9

= 34
Let’s Begin Use slope to determine whether the diagonals are
perpendicular.

3 – (–2) 5
Slope of BD = or –
Squares –1 – 2 3

2 – (–1) 3
Example Slope of AC = or – 5
3 – (–2)

Since the slope of AC is the negative reciprocal of
Determine whether parallelogram ABCD is a
rhombus, a rectangle, or a square for A(–2, –1), the slope of BD the diagonals are perpendicular.
B(–1, 3), C(3, 2), and D(2, –2). List all that apply. The lengths of AC and BD are the same so the
Explain.
diagonals are congruent. ABCD is a rhombus, a
rectangle, and a square.
B(–1, 3)
C(3, 2)
Examine
The diagonals are congruent and perpendicular so
ABCD must be a square. A square is also a
rhombus.

A(–2, –1)
D(2, –2) ABCD is a rhombus, a rectangle,
Answer
and a square.

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