6.4 Rhombuses, Rectangles, and Squares

Day 4

Review

Find the value of the variables.

52°

68°

h

p

(2p-14)° 50°

52° + 68° + h = 180°

120° + h = 180 °

h = 60°

p + 50° + (2p – 14)° = 180°p + 2p + 50° - 14° = 180° 3p + 36° = 180° 3p = 144 °

p = 48 °

Special Parallelograms

Rhombus A rhombus is a parallelogram with four

congruent sides.

Special Parallelograms

Rectangle A rectangle is a parallelogram with four right

angles.

Special Parallelogram

Square A square is a parallelogram with four

congruent sides and four right angles.

Corollaries

Rhombus corollary A quadrilateral is a rhombus if and only if it

has four congruent sides.

Rectangle corollary A quadrilateral is a rectangle if and only if it

has four right angles.

Square corollary A quadrilateral is a square if and only if it is a

rhombus and a rectangle.

Example

PQRS is a rhombus. What is the value of b?

P Q

RS

2b + 3

5b – 6

2b + 3 = 5b – 6 9 = 3b 3 = b

Review

In rectangle ABCD, if AB = 7f – 3 and CD = 4f + 9, then f = ___

A) 1

B) 2

C) 3

D) 4

E) 5

7f – 3 = 4f + 9

3f – 3 = 9

3f = 12

f = 4

Example

PQRS is a rhombus. What is the value of b?

P Q

RS

3b + 12

5b – 6

3b + 12 = 5b – 6 18 = 2b 9 = b

Theorems for rhombus

A parallelogram is a rhombus if and only if its diagonals are perpendicular.

A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

L

Theorem of rectangle

A parallelogram is a rectangle if and only if its diagonals are congruent.

A B

CD

Match the properties of a quadrilateral

1. The diagonals are congruent

2. Both pairs of opposite sides are congruent

3. Both pairs of opposite sides are parallel

4. All angles are congruent

5. All sides are congruent

6. Diagonals bisect the angles

A. Parallelogram

B. Rectangle

C. Rhombus

D. Square

B,D

A,B,C,D

A,B,C,D

B,D

C,D

C