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Quadrilaterals, Diagonals, and Angles of Polygons

Quadrilaterals, Diagonals, and Angles of Polygons. Quadrilaterals, Diagonals, and Angles of Polygons. A Polygon is a simple closed plane figure, having three or more line segments as sides A Quadrilateral is any four-sided closed plane figure

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Quadrilaterals, Diagonals, and Angles of Polygons

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  1. Quadrilaterals, Diagonals, and Angles of Polygons

  2. Quadrilaterals, Diagonals, and Angles of Polygons • A Polygon is a simple closed plane figure, having three or more line segments as sides • A Quadrilateral is any four-sided closed plane figure • A Diagonal is a line segment that connects one vertex to another (but not next to it) on a polygon

  3. Classifying Polygons

  4. Quadrilateral Angles • We know that the interior angles of a triangle add up to 180º • How many degrees are in the interior angles of a quadrilateral?

  5. Quadrilateral Angles • If we draw a diagonal from one vertex across to the opposite vertex, we see that we have formed two triangles • Therefore, the sum of two triangles will give you the measure of the interior angles of a quadrilateral • 180º + 180º = 360º

  6. Quadrilateral Angles Checkpoint • Find the missing angle of a quadrilateral with the following measures: m 1 = 117º m 2 = 110º m 3 = 75º m 4 = 117º + 110º + 75º + xº = 360º 302º + x = 360º x = 58º 58º

  7. Angles of Polygons Mini-Lab • Let’s explore this knowledge and how it relates to the angles of other polygons • Copy the table below:

  8. Angles of Polygons Mini-Lab • Draw a pentagon with diagonals from one vertex to each opposing vertex

  9. Angles of Polygons Mini-Lab • Let’s explore this knowledge and how it relates to the angles of other polygons • Copy and complete the table below:

  10. Angles of Polygons Mini-Lab • Draw a hexagon with diagonals from one vertex to each opposing vertex

  11. Angles of Polygons Mini-Lab • Let’s explore this knowledge and how it relates to the angles of other polygons • Copy and complete the table below:

  12. Angles of Polygons Mini-Lab • Draw a heptagon with diagonals from one vertex to each opposing vertex

  13. Angles of Polygons Mini-Lab • Let’s explore this knowledge in how it relates to the angles of other polygons • Copy and complete the table below:

  14. Angles of Polygons Mini-Lab • What patterns do you see as a result of our experiment? • The number of triangles in any polygon is always two less than the number of sides. • Therefore, if n = the number of sides of the polygon; the sum of interior angles of any polygon can be expressed as (n – 2)180º

  15. Angles of Polygons Checkpoint • Find the sum of the measures of the interior angles of each polygon: 15-gon? 23-gon? 30-gon? (15-sided figure) (23-sided figure) (30-sided figure) 13 x 180º = 2340º 21 x 180º = 3780º 28 x 180º = 5040º

  16. Regular Polygons • A regular polygon is one that is equilateral (all sides congruent) and equiangular (all angles congruent) • Polygons that are not regular are said to be irregular

  17. Regular Polygons • If the formula for finding the sum of measures of interior angles of a polygon is (n-2)180º, how would you find the measure of each angle of a regular polygon? ( n – 2 )180º n

  18. Regular Polygons Checkpoint • Find the sum of the measures of the interior angles of each regular polygon and the measure of each individual angle: 15-gon? 23-gon? 30-gon? (15-sided figure) (23-sided figure) (30-sided figure) 13 x 180º = 2340º 2340º / 15 = 156º 21 x 180º = 3780º 3780º / 23 = 164.35º 28 x 180º = 5040º 5040º/ 30 = 168º

  19. Homework • Skill 4: Polygons • 6-3 Skills Practice: Polygons and Angles • DUE TOMORROW!

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