Page 24 - Math Course 3 (Book 2)

Properties of Rectangles

The diagonals of a rectangle are congruent, so Diagonals of a Parallelogram
RT ≅ SU

RT ≅ SU Diagonals of a rectangle are ≅. Example

RT = SU Definition of congruent segments
Kyle is building a barn for his horse. He measures
6x + 4 = 7x – 4 Substitution the diagonals of the door opening to make sure that
they bisect each other and they are congruent. How
4 = x – 4 Subtract 6x from each side. does he know that the measure of each corner is
90?
8 = x Add 4 to each side. B C

Answer 8

Angles of a Rectangle
A D
Example

We know that AC ≅ BD.

Quadrilateral LMNP is a rectangle. Find x. A parallelogram with congruent
Answer diagonals is a rectangle.
S T Therefore, the corners are 90°
(6y + 2)° angles.

(5x + 8)° Your Turn!
Diagonals of a Rectangle
(3x + 2)° Quadrilateral EFGH is a rectangle.
R U If FH = 5x + 4 and GE = 7x – 6, find x.

A. x = –1 G H
∠MLP is a right angle, so m∠MLP = 90
B. x = 3
C. x = 5
Angle Addition D. x = 10
m∠MLN + m∠NLP = m∠MLP
Postulate
5x + 8 + 3x + 2 = 90 Substitution

8x + 10 = 90 Simplify.
Subtract 10 from
8x = 80
each side.
Divide each side F E
x = 10
by 8.

Answer 10 Answer

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