1. Objectives Vocabulary
Unit 6 – Polygons and Quadrilaterals 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

2. 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.

3. 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.

4. 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.

5. Polygon Angle Sum Theorem:
Unit 6 – Polygons and Quadrilaterals 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.

6. Find the measure of each interior angle of a regular 16-gon.
Unit 6 – Polygons and Quadrilaterals 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.

7. Find the measure of each interior angle of pentagon ABCDE.
Unit 6 – Polygons and Quadrilaterals 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°

8. Polygon ExteiorAngle Sum Theorem:
Unit 6 – Polygons and Quadrilaterals 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.  =

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

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

11. 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 .

12. Theorem: Opposite sides of a parallelogram are congruent.
Unit 6 – Polygons and Quadrilaterals 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

13.  Theorems: Opposite angles of a parallelogram are congruent.
Unit 6 – Polygons and Quadrilaterals 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

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

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

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

17. 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!