## Quadrilaterals: Rectangles and Squares

#### 1. Properties of Rectangles and Squares

A geometrical figure with 4 sides is a

The above figure is a rectangle. In a rectangle,

The above figure is a square. In a square,

**quadrilateral**.**Rectangles**and**squares**are quadrilaterals.The above figure is a rectangle. In a rectangle,

- Opposite sides are equal and parallel
- All angles are right angles (90°)

The above figure is a square. In a square,

- All sides are equal
- Opposite sides are parallel
- All angles are right angles (90°)

#### 2. Which of the following quadrilaterals are squares or rectangles and which are not?

Figure

Figure

**T**is a**square**.Figure

**U**is a**rectangle**.#### 3. Following quadrilaterals are squares or rectangles.

In each figure, find the lengths of the unknown sides.

**ABCD**is a rectangle.

AB = 6 cm

BC = 3 cm

Opposite sides of a rectangle are equal.

**EFGH**is a square.

FG = 10 cm

GH = 10 cm

All sides of a square are equal.

**JKLM**is a rectangle.

JK = 1.5 cm

KL = 4.5 cm

**PQRS**is a square.

QR = 4 cm

RS = 4 cm

#### 4. In the figures below, ABCD is a square and PQRS is a rectangle.

Find the unknown marked angles a and b.

In

**Square ABCD**,

**∠**ADC = 90°

45° +

**∠a**+ 23° = 90°

**∠a**= 90° − 45° − 23°

= 22°

In

**Rectangle PQRS**,

**∠**PQR = 90°

18° +

**∠b**+ 48° = 90°

**∠b**= 90° − 18° − 48°

= 24°

#### 5. The figure below is made of a rectangle ABCD and a square EFGH.

Find the length of BC.

In

**Square EFGH**,

EF = 7 cm − 2 cm

= 5 cm

GF = EF = 5 cm

BC = 3 cm + GF + 2 cm

= 3 cm + 5 cm + 2 cm

= 10 cm

BC = 3 cm + GF + 2 cm

= 3 cm + 5 cm + 2 cm

= 10 cm

All sides of a square are equal.

#### 6. All lines in the figure below meet at right angles.

Find the lengths of AB, EF and AL.

AB = 12 cm + 50 cm

= 62 cm

EF = 50 cm − 25 cm

= 25 cm

AL = 14 cm + 14 cm + 14 cm + 14 cm + 14 cm

= 70 cm