1. GOAL 1 DESCRIBING POLYGONS EXAMPLE 1 6.1 Polygons VOCABULARY polygon sides vertex convex nonconvex (concave) equilateral equiangular regular diagonal

2. Extra Example 1 EXAMPLE 2 Identify the figures that are not polygons. Explain. A B CD B: two sides intersect only one other side C: the sides intersect more than two other sides, some at nonendpoints.

3. Extra Example 2 EXAMPLE 3 Identify the polygon and state whether it is convex or concave. a. b. a. convex quadrilateralb. concave pentagon

4. Extra Example 3 Decide whether the polygon is regular. a. b. a. No; all angles do not have the same measure. b. No; all sides are not the same length.

5. Checkpoint State whether the figure is a polygon. If it is, state whether it is convex or concave. If it is not a polygon, explain why not. A B A: not a polygon because some sides are not segments B: concave octagon

6. GOAL 2 INTERIOR ANGLES OF QUADRILATERALS EXAMPLE 4 6.1 Polygons The sum of the measures of the interior angles of a quadrilateral is 360°. INTERIOR ANGLES OF A QUADRILATERAL Since the sum of the measures of each triangle is 180°, the sum of the measures of the interior angles of the quadrilateral is 360°.

7. Extra Example 4 55° x°x° x°x° EF GH Since we know that the sum of the measures of the angles of a quadrilateral is 360°, and angles E and G are congruent, we can write the following equation: x + x + 55 + 55 = 360 Solving the equation gives x = 125, so

8. Checkpoint Is quadrilateral JKLM regular? 80°x°x° x°x°(x - 20)° JK LM