COURSE 2 LESSON 7 6 Draw a Diagram

COURSE 2 LESSON 7 -6 Draw a Diagram and Look for a Pattern How many diagonals can be drawn inside a decagon? The goal is to find the number of diagonals that can be drawn inside a decagon. Remember that a diagonal is a segment that joins two vertices that are not endpoints of the same side of a polygon. The diagram below shows all the diagonals that can be drawn inside each polygon shown. 3 sides 4 sides 5 sides 7 -6 6 sides

COURSE 2 LESSON 7 -6 Draw a Diagram and Look for a Pattern (continued) Make a table to organize the information from the diagram. sides 3 4 5 6 diagonals 0 2 5 9 The data in the table indicates that the formula for the number of n(n – 3) diagonals that can be drawn inside a polygon of n sides is 2 For a decagon, n = 10. 10(10 – 3) 10 • 7 = 2 = 35 2 Thirty-five diagonals can be drawn inside a decagon. 7 -6

COURSE 2 LESSON 7 -6 Draw a Diagram and Look for a Pattern (continued) To check that 35 diagonals can be drawn inside a decagon, draw a diagram. There are 35 diagonals. 7 -6

COURSE 2 LESSON 7 -6 Draw a Diagram and Look for a Pattern Solve by drawing a diagram and looking for a pattern. The exterior angles of a triangle are the supplements of the interior angles, as shown. What is the sum of the exterior angles of a regular hexagon? 360º 7 -6