Review of A1 Standards

How Do I Classify and Find Angles In Polygons?

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

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.

Course 3

7-4 Classifying Polygons

6

5

8

900

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

Course 3

7-4 Classifying Polygons

Learn to classify and find angles in polygons.

Course 3

7-4 Classifying Polygons

Vocabularypolygon

regular polygon

trapezoid

parallelogram

rectangle

rhombus

square

Insert Lesson Title Here

Course 3

7-4 Classifying Polygons

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

Course 3

7-4 Classifying Polygons

nn-gon

8Octagon

7Heptagon

6Hexagon

5Pentagon

4Quadrilateral

3Triangle

Number of SidesPolygon

Course 3

7-4 Classifying Polygons

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

Divide the figure into triangles.

Course 3

7-4 Classifying Polygons

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

Divide the figure into triangles.

Course 3

7-4 Classifying Polygons

Find the sum of the angle measures in a heptagon.

5 • 180° = 900°

5 triangles

Check It Out: Example 1A

Divide the figure into triangles.

Course 3

7-4 Classifying 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.

Course 3

7-4 Classifying Polygons

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°

Course 3

7-4 Classifying Polygons

Check It Out: Example 2A

Find the angle measures in the regular polygon.

5 congruent angles

5a° = 180°(5 – 2)

5a° = 180°(3)

5a° = 540°

5a°5

540°5

=

a° = 108°

a°

a°a°

a°

a°

Course 3

7-4 Classifying Polygons

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

=

Course 3

7-4 Classifying 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°

Check It Out: Example 2B

Course 3

7-4 Classifying Polygons

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.

Course 3

7-4 Classifying Polygons

Course 3

7-4 Classifying Polygons

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.

Course 3

7-4 Classifying Polygons

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

Course 3

7-4 Classifying Polygons

Check It Out: 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

Course 3

7-4 Classifying Polygons

Give all the names that apply to the figure.

quadrilateral

Four-sided polygon

Check It Out: Example 3B

Course 3

7-4 Classifying Polygons

Lesson Quiz: Part 21. 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.

Insert Lesson Title Here

Course 3

7-4 Classifying Polygons

4. Find the missing angle measure in the acute triangle shown.

Lesson Quiz: Part 3

4. Find the missing angle measure in the acute triangle shown.

5. Find the missing angle measure in the right triangle shown.

Course 3

7-3 Angles in Triangles

Lesson Quiz: Part 3

5. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°.

6. Find the missing angle measures in the triangle below.

Course 3

7-3 Angles in Triangles

Lesson Quiz: Part II

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

below.

Insert Lesson Title Here

quadrilateral, rhombus, parallelogram

Course 3

7-4 Classifying Polygons