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Polygons 5.4 Pre-Algebra
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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
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Learn to classify and find angles in polygons.
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Vocabulary polygon regular polygon trapezoid parallelogram rectangle
rhombus square
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The cross section of a brilliant-cut diamond is a pentagon
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.
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Polygon Number of Sides 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon n n-gon
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Example: Finding Sums of the Angle Measures in Polygons
A. Find the sum of the angle measures in a hexagon. Divide the figure into triangles. 4 triangles 4 • 180° = 720°
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Example: Finding Sums of the Angle Measures in Polygons Continued
B. Find the sum of the angle measures in a octagon. Divide the figure into triangles. 6 triangles 6 • 180° = 1080°
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Try This A. Find the sum of the angle measures in a hexagon.
Divide the figure into triangles. 4 triangles 4 • 180° = 720°
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Try This B. Find the sum of the angle measures in a heptagon.
Divide the figure into triangles. 5 triangles 5 • 180° = 900°
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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.
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Example: 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°
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Example: 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° 4y 4 360°4 = y = 90°
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Try This Find the angle measures in the regular polygon.
5 congruent angles 5a = 180°(5 – 2) a° 5a = 180°(3) a° a° 5a = 540° 5a 5 540° = a° a° a = 108°
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Try This Find the angle measures in the regular polygon.
8 congruent angles b° 8b = 180°(8 – 2) 8b = 180°(6) 8b = 1080° 8b 8 1080° = b = 135°
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Example: Classifying Quadrilaterals
Give all the names that apply to the figure. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rectangle 4 right angles rhombus 4 congruent sides square 4 congruent sides and 4 right angles
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Example: Classifying Quadrilaterals Continued
Give all the names that apply to the figure. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rhombus 4 congruent sides
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Try This Give all the names that apply to the figure. A. quadrilateral
Four-sided polygon parallelogram 2 pairs of parallel sides rectangle 4 right angles
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Try This Give all the names that apply to the figure. B. quadrilateral
Four-sided polygon
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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°
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Lesson Quiz: Part 2 4. Write all of the names that apply to the figure below. quadrilateral, rhombus, parallelogram
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