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.

Regular polygon – all sides congruent and all angles congruent Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons Regular polygon – all sides congruent and all angles congruent Irregular polygon - not regular Concave - part of a diagonal contains points in the exterior of the polygon. Convex - If no diagonal contains points in the exterior.

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.

Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons For convex polygons… Sum of interior angles = (n – 2)∙180° where n = number of sides Sum of exterior angles = 360 °

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°

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

A quadrilateral with two pairs of parallel sides is a parallelogram. 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

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

nonagon; irregular; concave Unit 6 – Polygons and Quadrilaterals 6.1 Properties of Polygons 1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex. nonagon; irregular; concave 2. Find the sum of the interior angle measures of a convex 11-gon. 1620° 3. Find the measure of each interior angle of a regular 18-gon. 4. Find the measure of each exterior angle of a regular 15-gon. 160° 24° 5. Find the value of r in polygon JKLM. r = 15

mWLP = 144°. Find each measure. Unit 6 – Polygons and Quadrilaterals 6.2 Properties of Polygons In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure. 1. PW 2. mPNW 18 144° QRST is a parallelogram. Find each measure. 3. TQ 4. mT 28 71°

ASSIGNMENT: 6.1(398): 23,25,26,29,31,33,41,56 26)12 56)100,104,108,112,116   6.2(407): 29,30,32-43,47 30)6,36 32)∠RKM,opp ∠≌ 34)RT, diag bisect each other 36)RK, dfn 38) ∠RKP, AIA 40)180,consec ∠ supp 42)90,37,53 46)3,6