6/4/ : Analyzing Polygons 3.8: Analyzing Polygons with Coordinates G1.1.5: Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint. G1.4.2: Solve multistep problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry. G1.1.5: Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint. G1.4.2: Solve multistep problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry.

6/4/ : Analyzing Polygons Slope Slope is the measure of the steepness of a line. We often say slope is found by rise over run, although this is not the definition.

6/4/ : Analyzing Polygons Slope Defn: Given a line containing (x 1,y 1 ) and (x 2,y 2 ), the slope of the line is equal to: y 2 - y 1 x 2 - x 1

6/4/ : Analyzing Polygons In the standard (x,y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,-8)? A)-15 B)-1 C) -1 / 7 D) 21 / 32 E)15 In the standard (x,y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,-8)? A)-15 B)-1 C) -1 / 7 D) 21 / 32 E)15

6/4/ : Analyzing Polygons Parallel Lines and Slopes Theorem Two coplanar nonvertical lines are parallel iff they have ______ _________. Any 2 vertical lines are parallel.

6/4/ : Analyzing Polygons Perpendicular Lines and Slopes Theorem Two coplanar nonvertical lines are perpendicular iff the ___________ of their _______ is ____ (they are opposite reciprocals). Horizontal and vertical lines are perpendicular.

What is the slope of any line parallel to the line 2x – 3y = 7? 6/4/ : Analyzing Polygons

What is the slope of a line perpendicular to the line determined by the equation 7x + 4y = 11? A)-4 B) -7 / 4 C) 11 / 4 D)4 E) 4 / 7 What is the slope of a line perpendicular to the line determined by the equation 7x + 4y = 11? A)-4 B) -7 / 4 C) 11 / 4 D)4 E) 4 / 7 6/4/ : Slopes of Lines 8

6/4/ : Analyzing Polygons Show that the quadrilateral with vertices A(1,1), B(6,1), C(4,6) and D(2,6) is a trapezoid.

6/4/ : Analyzing Polygons The endpoints of 2 segments are given below. Determine if the segments are parallel, perpendicular or neither. (-2,1) and (1,-2); (-1,-1) and (3,3) The endpoints of 2 segments are given below. Determine if the segments are parallel, perpendicular or neither. (-2,1) and (1,-2); (-1,-1) and (3,3)

6/4/ : Analyzing Polygons A square has its vertices at W(0,0), X(4,0), Y(4,4) and Z(0,4). Prove the diagonals are perpendicular.

6/4/ : Analyzing Polygons Midpoint Formula The midpoint, M, of a segment with endpoints (x 1,y 1 ) and (x 2,y 2 ) and can be found using the formula: M= The midpoint, M, of a segment with endpoints (x 1,y 1 ) and (x 2,y 2 ) and can be found using the formula: M=

6/4/ : Analyzing Polygons Give the coordinates of the midpoint of AB if A(3,12) and B(9,-2).

The Distance Formula The distance between two points with coordinates (x 1, y 1 ) and (x 2, y 2 ) is given by: 6/4/ : Analyzing Polygons

In the standard (x,y) coordinate plane, what is the length of the line segment that has endpoints (-3,4) and (5,-6)? A)9 B)2√41 C)18 D)20√2 E)40 In the standard (x,y) coordinate plane, what is the length of the line segment that has endpoints (-3,4) and (5,-6)? A)9 B)2√41 C)18 D)20√2 E)40 6/4/ : Analyzing Polygons

6/4/ : Analyzing Polygons Prove the Triangle Midsegment Conjecture.

6/4/ : Analyzing Polygons Given triangle ABC with coordinates A(a,b), B(c,d) and C(e,b), the midpoints of AB and BC are M and N. Prove: 1. AC || MN 2. MN =.5AC Given triangle ABC with coordinates A(a,b), B(c,d) and C(e,b), the midpoints of AB and BC are M and N. Prove: 1. AC || MN 2. MN =.5AC

6/4/ : Analyzing Polygons

6/4/ : Analyzing Polygons Assignment pages , #12-18 (evens), (all), 24, 26, (evens except 42), 50 pages , #12-18 (evens), (all), 24, 26, (evens except 42), 50