9 ABCD has vertices (8,9),(9,3),(2,5) and (1,11) ABCD has vertices (8,9),(9,3),(2,5) and (1,11). What type of quadrilateral is ABCD? Justify. Find the perimeter and area of ABCDDACBTask 2
10 Justify It looks like a parallelogram Part 1That means distance formula Opposites are the Congruent (same/equal)So, AB = CD and BC =DA
11 Slopes- Opposites are equal (same) Justifying …Part 2Slopes- Opposites are equal (same)AB = CD and BC = DA
12 If the coordinates of MNOP are M(7,6),N(-6,1),O(-4,-3) and P(9,2), what type of quadrilateral is MNOP? Find the area and perimeter of MNOP.JustifyMNPJustifyOTask 3
13 Justify a Rectangle It appears to be a rectangle Need to show: Opposite sides are congruentDistance FormulaOpposite sides are parallelSlopes are equalAdjacent lines form right anglesPerpendicular Slopes
14 Justify a RectanglePart 1Distance Formula: prove NM OP, MP NO
15 Justify a Rectangle Part 2 Prove: Opposite sides are Parallel; They have the same Slopes.
16 Justify a Rectangle Part 3 Prove adjacent lines form right angles; Show Perpendicular slopesThey are not perpendicular!Quadrilateral MNOP is not a Rectangle !
19 Prove MATH is a trapezoid. Find the area and perimeter. Task 5
20 Find the equation of a line that includes an altitude of parallelogram MATH. JustifyTask 8
21 Say What!? Write the equation of a line perpendicular. Let’s choose segment MH.Let’s use point A
22 Altitude Steps: Find the slope of the segment Write the perpendicular slopeUse coordinate AI suggest point slope formulaSimplify it into slope intercept form
23 Connect the midpoints of the sides of ABCD consecutively to form a new quadrilateral. Which special quadrilateral is it? Justify. How large are the perimeter and area of the new figure in comparison to the same measures for ABCD?Task 11
24 Thus ends the Quadrilateral portion of proving shapes are what they appear to be.