1. WARM UP Each table will write their definition on the white board as follows: Table 1: Linear Pair of angles Table 2: Acute angle Table 3: Obtuse angle Table 4: Complementary angles Table 5: Supplementary angles Table 6: Vertical angles Table 8: Right angle

2. WARM UP Each table will have five minutes to come up with a counterexample for the tables’ definition as follows: Table 1: Table 3’s Table 2: Table 8’s Table 3: Table 5’s Table 4: Table 1’s Table 5: Table 6’s Table 6: Table 4’s Table 8: Table 2’s

3. SOLUTIONS/DEFINITIONS Each table will write their definition on the white board as follows: 1)A right angle is an angle that measures 90°. 2)An acute angle measures less than 90°. 3)An obtuse angle measures more than 90° but less than 180°. 4)A pair of complementary angles has a sum of 90° 5)A pair of supplementary angles has a sum of 180°. 6)Vertical angles are angles formed by two intersecting lines; they share a common vertex but not a common side. 7)Two angles are a linear pair if they share a common vertex and a common side and their noncommon sides form a line.

4. POLYGONS

5. OBJECTIVES Define and classify polygons and related terms. Practice writing definitions. Learn even more vocabulary. Develop critical thinking and cooperative behavior.

6. DEFINITIONS A polygon is a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. Each line segment is called a side of the polygon. Each endpoint where the sides meet is called a vertex of the polygon.

7. CLASSIFYING POLYGONS You classify a polygon by the number of sides it has. Familiar polygons have specific names, listed in the the table. The ones without specific names are called n-sided polygons, or n-gons. For instance you call a 25-sided polygons and 25-gon.

8. NAMING POLYGONS To name a polygon, list the vertices in consecutive order. You can also name the pentagon to the below pentagon ABCDE. You can also call it DCBAE but not BCAED. When the polygon is a triangle, you use the triangle symbol. For example ΔABC means triangle ABC.

9. NAMING POLYGONS A diagonal of a polygon is a line segment that connects two nonconsecutive vertices. A polygon is convex if no diagonal is outside the polygon. A polygon is concave if at least one diagonal is outside the polygon.

10. NAMING POLYGONS Recall that two segments or two angles are congruent if an only if they have the same measures. “Two polygons are congruent if and only if they are exactly the same size and shape. “If and only if” means that the statements work both ways.

11. NAMING POLYGONS For example, if quadrilateral CAMP is congruent to quadrilateral SITE, then their four pairs of corresponding angles and four pairs of corresponding sides are also congruent. When you write a statement of congruence, always write the letters of the corresponding vertices in an order that shows the correspondences.

12. EXAMPLE Which polygon is congruent to ABCDE? ABCDE ≅ _________ SOLUTION: Polygons JKFGH and ABCDE have all corresponding angles congruent, but not all corresponding sides. Polygons STUVW and ABCDE have all corresponding sides congruent but not all corresponding angles. All corresponding sides and angles must be congruent, so ABCDE ≅ NPQLM. You could also say ABCDE ≅ NMLQP because all the congruent parts would still match.

13. PERIMETER The perimeter of a polygon equals the sum of the lengths of its sides. Perimeter measures the length of the boundary of a two-dimensional figure. The quadrilateral below has a perimeter of 37 cm.

14. INVESTIGATION #4 SPECIAL POLYGONS Write a good definition of each of the items in your investigation sheets. Agree on a common set of definitions for your class and add them to your definitions list. Draw and label a figure to illustrate each definition.

15. CH. 1.4 ASSIGNMENTS Investigation #4 CP. 1.4