Warm UP: Identifying Polygons

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Presentation transcript:

Warm UP: Identifying Polygons State whether the figure is a polygon. If it is not, explain why. Not D – has a side that isn’t a segment – it’s an arc. Not E– because two of the sides intersect only one other side. Not F because some of its sides intersect more than two sides/ Figures A, B, and C are polygons.

Polygons are named by the number of sides they have – MEMORIZE Type of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon

Polygons are named by the number of sides they have – MEMORIZE Type of Polygon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

Convex or concave? CONCAVE CONVEX Identify the polygon and state whether it is convex or concave. CONCAVE CONVEX

Identifying Regular Polygons Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon. Decide whether the following polygons are regular. Pentagon is equilateral and equiangular, so it is a regular polygon. Equilateral, but not equiangular, so it is NOT a regular polygon.

6.1 Polygons Objectives: Identify, name, and describe polygons Use the sum of the measures of the interior angles of a quadrilateral.

Theorem 6.1: Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360°. m1 + m2 + m3 + m4 = 360°

Ex. 1: Use the information in the diagram to solve for x. 80° 70° 2x° x° x°+ 2x° + 70° + 80° = 360° 3x + 150 = 360 3x = 210 x = 70 Sum of the measures of int. s of a quadrilateral is 360° Combine like terms Subtract 150 from each side. Divide each side by 3.

Ex. 2: Use the information in the diagram to solve for x. 5x + 7x + 50 + 70 = 360 12x + 120 = 360 12x = 240 X = 20 50 7x 5x 70

Ex. 3: Use the information in the diagram to solve for x. 87 93

Ex. 4: Use the information in the diagram to solve for x. 3x + 2x + 3x + 2x = 360 10x = 360 x = 36 2x 3x 3x 2x

Ex. 5: Find the measure of each angle in the parallelogram. 2x + 4x +2x + 4x = 360 12x = 360 x = 30 Substitute 2(30) = 60 4 (30) = 120 2x 4x 2x 4x

Assignment Solve the remaining problems independently Reminder: 2nd Nine weeks benchmark on Thursday