In Class: pg 405 #30. HW Requests: HW: pg 404 #11-21; 414 #9,11,13,19,21,23,25,27 Parallelogram WS: Due Thurs. Required Honors EC - Regular
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1 5/28/13 HR Section 6.1/6.2 Polygons Obj: SWBAT recognize & apply properties of the sides, diagonals & angles of parallelograms. Bell Ringer: pg 405 #31-36 In Class: pg 405 #30 HW Requests: HW: pg 404 #11-21; 414 #9,11,13,19,21,23,25,27 Parallelogram WS: Due Thurs. Required Honors EC - Regular
2 1. Def n: Both pairs of opposite sides are parallel 2. Opp. Sides of are 3. Opp. s of are 4. Consecutive s are supplementary. 5. Diagonals of bisect each other. 6. Diagonal separates into 2 s Properties of Parallelograms In Class: Red WB pg 73
3 Properties of Parallelograms 1. Def n: Both pairs of opposite sides are parallel 2. Opp. Sides of are 3. Opp. s of are 4. Consecutive s are supplementary. 5. Diagonals of bisect each other. 6. Diagonal separates into 2 s Tests for Parallelograms. 1. Show that both pairs of opp. sides are 2. Show that both pairs of opp. Sides are 3. Show that both pairs of opp. s are 4. Show that diagonals bisect each other. 5. Show that one pair of opp. sides is and
4 Tests for Parallelograms. 1. Both pairs of opp. sides are 2. Both pairs of opp. s are 3. Diagonals bisect each other. 4. One pair of opp. sides is and 5. Both pairs of opp. sides are Ex. 3 Determine whether the figure with the given vertices is a. Use the method indicated. L(2,5), M(6,6), O(4,0), P(0,-1) 1. Slope Method tests both pairs of opp. sides 2. Slope and Distance Method - One pair of opp. sides is and
5 L M P O Determine whether the figure with the given vertices is a parallelogram. L(2,5), M(6,6), O(4,0), P(0, -1)? 1. Slope Method Slope and Distance Method
6 Tests for Parallelograms. 1. Both pairs of opp. sides are 2. Both pairs of opp. s are 3. Diagonals bisect each other. 4. One pair of opp. sides is and 5. Both pairs of opp. sides are Ex. 1 Determine whether the quadrilateral is a. Justify your answer. Ex. 2 Find x & y so each quad. is a.
7 Exit Ticket: pg 403 #1-8 Properties of Parallelograms 1. Opp. Sides of are 2. Opp. s of are 3. Consecutive s are supplementary. 4. Diagonals of bisect each other. 5. Diagonal separates into 2 s Tests for Parallelograms. 1. Both pairs of opp. Sides are 2. Both pairs of opp. s are 3. Diagonals bisect each other. 4. One pair of opp. sides is and
8 Exterior Angle Start at vertex and extend a side. Exterior Angle Sum Thm. Sum of exterior s (one at each vertex) = 360 Pg 407 #10,
9 A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
10 Exit Ringer: pg 407 #11, pg 414 #4-11
11 Sum of measures of interior s of convex polygon. Interior Angle Sum Theorem - For all polygons Sum interior s = 180 (number of sides -2) S = Sum interior s n = number of sides S = 180(n-2) (Regular Polygons) S =n * (minterior) 180(n-2) = n* (minterior)
12 Polygons Name: Date: Per: Name each polygon and tell how many sides it has. Circle regular or irregular to describe the polygon. From one vertex draw all diagonals. How many triangles result? What is the sum of all of the angles? Name # of sides Regular/ Irregular # of triangles Angle Sum Name # of sides Regular/ Irregular # of triangles Angle Sum Name # of sides Regular/ Irregular # of triangles Angle Sum Name # of sides Regular/ Irregular # of triangles Angle Sum Name # of sides Regular/ Irregular # of triangles Angle Sum Name # of sides Regular/ Irregular # of triangles Angle Sum
13 N-gon - n sided polygon See page 404 in text Regular Polygons All angles are. All sides are Convex Polygons All interior angles < 180 If lines are drawn containing each side no points on the line is in the interior. Diagonal connects any two nonconsecutive vertices.
14 Find number of sides given interior angle of regular polygon S = 180(n-2) Interior (int.)angle Sum Thm. For a regular polygon (why?) Sum int. s = (mint.) (number of sides) (draw figure) S = sum of int. s, n = number of sides S= (mint.) n and S = 180(n-2) (mint.)n=180 (n -2) Pg 407 #6
15 For any polygon, find the measure of each interior angle. A C = 5x B D = 11x+4 Pg 407 #8
16 Find number of sides given interior angle of regular polygon (m Int.)n = 180(n-2) Example 2 Sides of a Polygon The measure of an interior angle of a regular polygon is 135. Find the number of sides of the polygon. pg 407 #5, 6 for practice
17 Find number of sides given interior angle of regular polygon S = 180(n-2) Interior (int.)angle Sum Thm For a regular polygon (why?) Sum int. s = (mint.) (number of sides) (mint.)(number of sides)=180 (number of sides -2) (m Int.)n = 180(n-2)
18 N-gon - n sided polygon Regular Polygons All angles are. All sides are Convex Polygons All interior angles < 180 If lines are drawn containing each side no points on the line is in the interior. Diagonal
19
20 Regular Polygons All angles are. All sides are Convex Polygons All interior angles < 180 If lines are drawn containing each side no points on the line is in the interior. Irregular Polygons Angles are not Sides are not Concave Polygons Diagonal At least one interior angle > 180 If lines are drawn containing each side lines pass through interior.
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