7-4 Classifying Polygons Course 3 Warm Up Problem of the Day Lesson Presentation
7-4 Classifying Polygons
Course 3
Warm Up
Problem of the Day
Lesson 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
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
Divide the figure into triangles.
Course 3
7-4 Classifying Polygons
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
Divide the figure into triangles.
Course 3
7-4 Classifying Polygons
Check It Out: Example 1A
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
Find the sum of the angle measures in a heptagon.
5 • 180° = 900°
5 triangles
Check It Out: Example 1B
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
Additional 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
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
=
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
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
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.
Course 3
7-4 Classifying Polygons
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
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 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.
Insert Lesson Title Here
360°
720°
135°
Course 3
7-4 Classifying Polygons
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