1. Pre-Algebra 5-4 Polygons 5-4 Polygons Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. 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

3. 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

4. Pre-Algebra 5-4 Polygons Learn to classify and find angles in polygons.

5. Pre-Algebra 5-4 Polygons Vocabulary polygon regular polygon trapezoid parallelogram rectangle rhombus square

6. 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.

7. Pre-Algebra 5-4 Polygons nn-gon 8Octagon 7Heptagon 6Hexagon 5Pentagon 4Quadrilateral 3Triangle Number of Sides Polygon

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. Pre-Algebra 5-4 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 66x 6 720° 6 = x = 120°

14. Pre-Algebra 5-4 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 44y 4 360° 4 =

15. 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° 5a55a5 540° 5 = a = 108° a°

16. 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 88b 8 1080° 8 = b = 135° b° Try This: Example 2B

17. Pre-Algebra 5-4 Polygons

18. 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.

19. Pre-Algebra 5-4 Polygons Additional 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

20. 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.

21. Pre-Algebra 5-4 Polygons Give all the names that apply to the figure. quadrilateral Four-sided polygon B. Try This: Example 3B

22. 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°

23. Pre-Algebra 5-4 Polygons Lesson Quiz: Part 2 4. Write all of the names that apply to the figure below. quadrilateral, rhombus, parallelogram