Polygons9-4

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Polygons9-4

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.

6

5

8

900

Polygons9-4

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

Polygons9-4

MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180 degrees and apply this fact to find…the sum of angles in polygons.

Sunshine State Standards

Polygons9-4

Vocabularypolygon

regular polygon

trapezoid

parallelogram

rectangle

rhombus

square

Polygons9-4

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

Polygons9-4

nn-gon

8Octagon

7Heptagon

6Hexagon

5Pentagon

4Quadrilateral

3Triangle

Number of SidesPolygon

Polygons9-4

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

Find the sum of the angle measures in a hexagon.

4 • 180° = 720°

4 triangles

Draw diagonals to divide the figure into triangles.

Polygons9-4

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

Find the sum of the angle measures in a octagon.

6 • 180° = 1080°

6 triangles

Draw diagonals to divide the figure into triangles.

Polygons9-4

Check It Out: Example 1

Find the sum of the angle measures in a heptagon.

5 • 180° = 900°

5 triangles

Draw diagonals to divide the figure into triangles.

Polygons9-4

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.

Polygons9-4

Additional Example 2A: Finding the Measure of Each Angle in a Regular Polygon

Find the angle measures in the regular polygon.

8 congruent angles

8x° = 180°(8 – 2)

8x° = 180°(6)

8x° = 1080°

8x° 8

1080°8

=

x° = 135°

Polygons9-4

Additional 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

=

Polygons9-4

Check It Out: Example 2

Find the angle measures in the regular polygon.

9 congruent angles

9y° = 180°(9 – 2)

9y° = 180°(7)

9y° = 1260°

9y°9

1260°9

=

y° = 140°

Polygons9-4

Quadrilaterals with certain properties are given additional names. A trapezoid has exactly 1 pair of parallel sides. A parallelogram has 2 pairs of parallel sides. A rectangle has 4 right angles. A rhombus has 4 congruent sides. A square has 4 congruent sides and 4 right angles.

Polygons9-4

Polygons9-4

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.

Polygons9-4

Additional Example 3B: Classifying Quadrilaterals

Give all the names that apply to the figure.

quadrilateral

parallelogram

rhombus

Four-sided polygon

2 pairs of parallel sides

4 congruent sides

Polygons9-4

Check It Out: Example 3A

Give all the names that apply to each figure.

Quadrilateral – 4 sided polygon Trapezoid – 1 pair of parallel sides

Polygons9-4

Give all the names that apply to each figure.

Quadrilateral – 4 sided polygon Parallelogram – 2 pairs of parallel sides Rhombus – 4 congruent sides

Check It Out: Example 3B

Polygons9-4

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Polygons9-4

Lesson Quiz: Part I

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°

Polygons9-4

Lesson Quiz: Part II

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

below.

quadrilateral, rhombus, parallelogram

Polygons9-4

1. Identify the sum of the angle measures in a heptagon.

A. 520°

B. 540°

C. 720°

D. 900°

Lesson Quiz for Student Response Systems

Polygons9-4

2. Identify the sum of the angle measures in a 17-gon.

A. 1800°

B. 2700°

C. 3060°

D. 3600°

Lesson Quiz for Student Response Systems

Polygons9-4

3. Identify all the names that apply to the given figure.

A. parallelogram, rectangle

B. trapezoid, quadrilateral

C. rhombus, square, trapezoid

D. rectangle, quadrilateral, trapezoid

Lesson Quiz for Student Response Systems