Objectives Vocabulary Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Objectives 1. Classify polygons based on their sides and angles. 2. Find and use the measures of interior and exterior angles of polygons. Vocabulary side of a polygon vertex of a polygon diagonal regular polygon concave convex

Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints. Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular. A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.

Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

Polygon Angle Sum Theorem: Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Polygon Angle Sum Theorem: The sum of the interior angle measures of a convex polygon equals (n-2)∙180° where n = number of sides. Find the sum of the interior angle measures of a convex heptagon. (n – 2)180° Polygon  Sum Thm. (7 – 2)180° A heptagon has 7 sides, so substitute 7 for n. 900° Simplify.

Find the measure of each interior angle of a regular 16-gon. Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Find the measure of each interior angle of a regular 16-gon. Step 1 Find the sum of the interior angle measures. (n – 2)180° Polygon  Sum Thm. (16 – 2)180° = 2520° Step 2 Find the measure of one interior angle. The int. s are , so divide by 16.

Find the measure of each interior angle of pentagon ABCDE. Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Find the measure of each interior angle of pentagon ABCDE. Polygon  Sum Thm. (5 – 2)180° = 540° mA + mB + mC + mD + mE = 540° 35c + 18c + 32c + 32c + 18c = 540 135c = 540 mA = 35(4°) = 140° c = 4 mB = mE = 18(4°) = 72° mC = mD = 32(4°) = 128°

Polygon ExteiorAngle Sum Theorem: Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Polygon ExteiorAngle Sum Theorem: The sum of the exterior angles (one at each vertex) of a convex polygon equals 360° Note: The number of sides doesn’t matter Find the measure of each exterior angle of a regular 20-gon. A 20-gon has 20 sides and 20 vertices. sum of ext. s = 360°. measure of one ext.  =

Find the value of b in polygon FGHJKL. Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Find the value of b in polygon FGHJKL. 15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360° 120b = 360 b = 3

Objectives 6.2 Properties of Parallelograms Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems. 6-2

Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol .

Theorem: Opposite sides of a parallelogram are congruent. Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons Theorem: Opposite sides of a parallelogram are congruent. A B C D Given: ABCD is a parallelogram Prove: AB  CD and BC  AD

 Theorems: Opposite angles of a parallelogram are congruent. Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons Theorems: Opposite angles of a parallelogram are congruent. Consecutive angles are supplementary. Diagonals bisect each other. You know what's coming next…  Prove ‘em! Prove ‘em all

In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Find mEFC. Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Find mEFC. Find DF.

WXYZ is a parallelogram. Find YZ. Find mZ . Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons WXYZ is a parallelogram. Find YZ. Find mZ . Find mY . Find mX .

EFGH is a parallelogram. Find JG. Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons 2x+8 3y-6 3x-y 2y-9 F G H J E EFGH is a parallelogram. Find JG. Find FH.

HOMEWORK: 6.1(398): 22-26,29,31-36,42,56,58 6.2(407): 29,30,32-43,46,47,52,54 Show work to receive credit!