Pre-Algebra

5-4 Polygons

5-4 Polygons

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

5-4 Polygons

Warm Up

1. How many sides does a hexagon have?

2. How many sides does a pentagon have?

3. How many angles does an octagon have?

4. Evaluate (n – 2)180 for n = 7.

Pre-Algebra

5-4 Polygons

6

5

8

900

Pre-Algebra

5-4 Polygons

Problem of the Day

Jeffrey planted four carnations, three dahlias, seven marigolds, five cornflowers, one geranium, and four mums. He forgot to water them and on each of the two following days, half the remaining flowers died. How many flowers were still living at the end of the second day? 6

Pre-Algebra

5-4 Polygons

Learn to classify and find angles in polygons.

Pre-Algebra

5-4 Polygons

Vocabularypolygon

regular polygon

trapezoid

parallelogram

rectangle

rhombus

square

Pre-Algebra

5-4 Polygons

The cross section of a brilliant-cut diamond is a pentagon. The most beautiful and valuable diamonds have precisely cut angles that maximize the amount of light they reflect.

A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides.

Pre-Algebra

5-4 Polygons

nn-gon

8Octagon

7Heptagon

6Hexagon

5Pentagon

4Quadrilateral

3Triangle

Number of SidesPolygon

Pre-Algebra

5-4 Polygons

Additional Example 1A: Finding Sums of the Angle Measures in Polygons

A. Find the sum of the angle measures in a hexagon.

4 • 180° = 720°

4 triangles

Divide the figure into triangles.

Pre-Algebra

5-4 Polygons

Additional Example 1B: Finding Sums of the Angle Measures in Polygons Continued

B. Find the sum of the angle measures in a octagon.

6 • 180° = 1080°

6 triangles

Divide the figure into triangles.

Pre-Algebra

5-4 Polygons

Try This: Example 1A

A. Find the sum of the angle measures in a hexagon.

4 • 180° = 720°

4 triangles

Divide the figure into triangles.

Pre-Algebra

5-4 Polygons

B. Find the sum of the angle measures in a heptagon.

5 • 180° = 900°

5 triangles

Try This: Example 1B

Divide the figure into triangles.

Pre-Algebra

5-4 Polygons

The pattern is that the number of triangles is always 2 less than the number of sides. So an n-gon can be divided into n – 2 triangles. The sum of the angle measures of any n-gon is 180°(n – 2).

All the sides and angles of a regular polygon have equal measures.

Pre-Algebra

5-4 PolygonsAdditional Example 2A: Finding the Measure of Each

Angle in a Regular Polygon

Find the angle measures in the regular polygon.

6 congruent angles

6x = 180°(6 – 2)

6x = 180°(4)

6x = 720°

6x 6

720°6

=

x = 120°

Pre-Algebra

5-4 PolygonsAdditional Example 2B: Finding the Measure of Each

Angle in a Regular Polygon

Find the angle measures in the regular polygon.

4 congruent angles

4y = 180°(4 – 2)

4y = 180°(2)

4y = 360°

y = 90°

4y 4

360°4

=

Pre-Algebra

5-4 Polygons

Try This: Example 2A

Find the angle measures in the regular polygon.

5 congruent angles

5a = 180°(5 – 2)

5a = 180°(3)

5a = 540°

5a5

540°5

=

a = 108°

a°

a°a°

a°

a°

Pre-Algebra

5-4 Polygons

Find the angle measures in the regular polygon.

8 congruent angles

8b = 180°(8 – 2)

8b = 180°(6)

8b = 1080°

8b 8

1080° 8

=

b = 135°

b°

b°

b° b°

b°

b°

b°b°

Try This: Example 2B

Pre-Algebra

5-4 Polygons

Pre-Algebra

5-4 Polygons

Additional Example 3A: Classifying Quadrilaterals

quadrilateral

parallelogram

rectangle

rhombus

square

Four-sided polygon

2 pairs of parallel sides

4 right angles

4 congruent sides

4 congruent sides and 4 right angles

Give all the names that apply to the figure.

Pre-Algebra

5-4 PolygonsAdditional Example 3B: Classifying Quadrilaterals

Continued

Give all the names that apply to the figure.

quadrilateral

parallelogram

rhombus

Four-sided polygon

2 pairs of parallel sides

4 congruent sides

Pre-Algebra

5-4 Polygons

Try This: Example 3A

Give all the names that apply to the figure.

quadrilateral

parallelogram

rectangle

Four-sided polygon

2 pairs of parallel sides

4 right angles

A.

Pre-Algebra

5-4 Polygons

Give all the names that apply to the figure.

quadrilateral

Four-sided polygon

B.

Try This: Example 3B

Pre-Algebra

5-4 Polygons

Lesson Quiz: Part 1

1. Find the sum of the angle measures in a

quadrilateral.

2. Find the sum of the angle measures in a

hexagon.

3. Find the measure of each angle in a regular

octagon.

360°

720°

135°

Pre-Algebra

5-4 Polygons

Lesson Quiz: Part 2

4. Write all of the names that apply to the figure

below.

quadrilateral, rhombus, parallelogram