Mathematics exam 3 doc

the sum of its interior angles will equal 180 + 180 = 360

degrees.

m∠a + m∠b + m∠c + m∠d = 360°

Interior Angles

To find the sum of the interior angles of any polygon, use

this formula:

S = 180(x − 2)°, with x being the number of

polygon sides

Example

Find the sum of the angles in this polygon:

S = (5 − 2) × 180°

S = 3 × 180°

S = 540°

Exterior Angles

Similar to the exterior angles of a triangle, the sum of the

exterior angles of any polygon equals 360 degrees.

Similar Polygons

If two polygons are similar, their corresponding angles

are equal and the ratios of the corresponding sides are in

proportion.

Example

These two polygons are similar because their

angles are equal and the ratios of the correspon￾ding sides are in proportion.

Parallelograms

A parallelogram is a quadrilateral with two pairs of par￾allel sides.

In the figure above, line AB || CD and BC || AD.

A parallelogram has:

■ opposite sides that are equal (AB = CD

and BC = AD)

■ opposite angles that are equal (m∠a = m∠c

and m∠b = m∠d)

■ consecutive angles that are supplementary (m∠a

+ m∠b = 180°, m∠b + m∠c = 180°, m∠c + m∠d

= 180°, m∠d + m∠a = 180°)

SPECIAL TYPES OF PARALLELOGRAMS

■ A rectangle is a parallelogram that has four right

angles.

A D

B C

AB = CD

A D

B C

60°

10

4

6

18

120°

60°

5 120°

2

3

9

b

c

e d

a

b

d

a c

–MEASUREMENT AND GEOMETRY–

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