Page 23 - Math Course 3 (Book 2)

Properties of Rectangles
Mo. 7

Lesson 4 Key Concept

KEY CONCEPTS: Rectangle

1. Recognize and apply properties of Words A rectangle is a quadrilateral with four right
rectangles. angles.
2. Determine whether parallelograms are
rectangles Properties Examples
1. Opposite sides
are congruent and AB ≅ DC AB || DC
parallel.
MO. 7 - L4a BC ≅ AD BC || AD
2. Opposite angles are
Recognizing the Properties of congruent. ∠A ≅ ∠C
∠B ≅ ∠D
Rectangles 3. Consecutive angles m∠A + m∠B = 180

are supplementary. m∠B + m∠C = 180
m∠C + m∠D = 180
Vocabulary A-Z m∠D + m∠A = 180

Let us learn some vocabulary 4. Diagonals are AC ≅ BD
congruent and
bisect each other. AC and BD bisect each
other.
rectangle 5. All four angles are
A four-sided quadrilateral where every angle is a right angles. m∠DAB = m∠BCD =
right angle (90°). Also opposite sides are parallel m∠ABC = m∠ADC = 90
and of equal length.
B C
A B

AC ≅ BD A D

D C Let’s Begin

THEOREMS

7.13 If a parallelogram is a rectangle, then the
diagonals are congruent. Diagonals of a Rectangle

Abbreviation: If ▱ is rectangle, diag. Example
are ≅.
A B
Quadrilateral RSTU is a rectangle. If RT = 6x + 4
AC ≅ BD and SU = 7x – 4, find x.

D C S T
7.14 If the diagonals of a parallelogram are con-
gruent, then the parallelogram is rectangle.

Abbreviation: If diagonals of ▱ are ≅,
▱ is a rectangle.
A B
AC ≅ BD R U
D C
15