pre-algebra 5-4 polygons 5-4 polygons pre-algebra warm up warm up problem of the day problem of the...
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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