Transcript Slide 1
Polygons 5.4 Pre-Algebra Warm Up 1. How many sides does a hexagon have? 6 2. How many sides does a pentagon have? 5 3. How many angles does an octagon have? 8 4. Evaluate (n – 2)180 for n = 7. 900 Learn to classify and find angles in polygons. Vocabulary polygon regular polygon trapezoid parallelogram rectangle rhombus square 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. Polygon Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 n-gon n 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° 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° Try This A. Find the sum of the angle measures in a hexagon. Divide the figure into triangles. 4 triangles 4 • 180° = 720° Try This B. Find the sum of the angle measures in a heptagon. Divide the figure into triangles. 5 triangles 5 • 180° = 900° 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. 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 = 720° 6 6 x = 120° 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 = 360° 4 4 y = 90° Try This Find the angle measures in the regular polygon. 5 congruent angles 5a = 180°(5 – 2) a° a° a° 5a = 180°(3) 5a = 540° a° a° 5a = 540° 5 5 a = 108° Try This Find the angle measures in the regular polygon. 8 congruent angles b° b° b° 8b = 180°(8 – 2) b° b° b° b° b° 8b = 180°(6) 8b = 1080° 8b = 1080° 8 8 b = 135° 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 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 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 Try This Give all the names that apply to the figure. B. quadrilateral Four-sided polygon Lesson Quiz: Part 1 1. Find the sum of the angle measures in a quadrilateral. 360° 2. Find the sum of the angle measures in a hexagon. 720° 3. Find the measure of each angle in a regular octagon. 135° Lesson Quiz: Part 2 4. Write all of the names that apply to the figure below. quadrilateral, rhombus, parallelogram