Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Sunshine State Standards MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180 degrees and apply this fact to find…the sum of angles in polygons.

Vocabulary polygon regular polygon trapezoid parallelogram rectangle rhombus square

A polygon is a closed plane figure formed by three or more segments 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 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon n n-gon

Additional Example 1A: Finding Sums of the Angle Measures in Polygons Find the sum of the angle measures in a hexagon. Draw diagonals to divide the figure into triangles. 4 triangles 4 • 180° = 720°

Additional Example 1B: Finding Sums of the Angle Measures in Polygons Continued Find the sum of the angle measures in a octagon. Draw diagonals to divide the figure into triangles. 6 triangles 6 • 180° = 1080°

Check It Out: Example 1 Find the sum of the angle measures in a heptagon. Draw diagonals to 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.

Additional Example 2A: Finding the Measure of Each Angle in a Regular Polygon Find the angle measures in the regular polygon. 8 congruent angles 8x° = 180°(8 – 2) 8x° = 180°(6) 8x° = 1080° 8x° 8 1080°8 = x° = 135°

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° 4y° 4 360°4 = y° = 90°

Check It Out: Example 2 Find the angle measures in the regular polygon. 9 congruent angles 9y° = 180°(9 – 2) 9y° = 180°(7) 9y° = 1260° 9y° 9 1260° = y° = 140°

Quadrilaterals with certain properties are given additional names Quadrilaterals with certain properties are given additional names. A trapezoid has exactly 1 pair of parallel sides. A parallelogram has 2 pairs of parallel sides. A rectangle has 4 right angles. A rhombus has 4 congruent sides. A square has 4 congruent sides and 4 right angles.

Additional Example 3A: 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

Additional Example 3B: Classifying Quadrilaterals Give all the names that apply to the figure. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rhombus 4 congruent sides

Check It Out: Example 3A Give all the names that apply to each figure. Quadrilateral – 4 sided polygon Trapezoid – 1 pair of parallel sides

Check It Out: Example 3B Give all the names that apply to each figure. Quadrilateral – 4 sided polygon Parallelogram – 2 pairs of parallel sides Rhombus – 4 congruent sides

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 21

Lesson Quiz: Part I 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°

Lesson Quiz: Part II 4. Write all of the names that apply to the figure below. quadrilateral, rhombus, parallelogram

Lesson Quiz for Student Response Systems 1. Identify the sum of the angle measures in a heptagon. A. 520° B. 540° C. 720° D. 900° 24

Lesson Quiz for Student Response Systems 2. Identify the sum of the angle measures in a 17-gon. A. 1800° B. 2700° C. 3060° D. 3600° 25

Lesson Quiz for Student Response Systems 3. Identify all the names that apply to the given figure. A. parallelogram, rectangle B. trapezoid, quadrilateral C. rhombus, square, trapezoid D. rectangle, quadrilateral, trapezoid 26