Classifying Quadrilaterals On a Cartesian Plane

Classify Quadrilateral We will be classifying five types of quadrilaterals Rectangle Square Rhombus Parallelogram Trapezoid

Rectangles Opposite sides are congruent Distance Formula Opposite sides are parallel Slopes Adjacent lines form right angles

Squares All sides are congruent Distance Formula Opposite sides are parallel Slope Adjacent lines form right angles Slopes

Rhombus All sides are congruent Distance Formula Opposite sides are parallel Slope

Parallelograms Opposite sides form parallel lines Slopes Opposite sides are congruent Distance Formula

Only one set of parallel lines Trapezoid Only one set of parallel lines Slope

Practice

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 ABCD D A C B Task 2

Justify It looks like a parallelogram Part 1 That means distance formula Opposites are the Congruent (same/equal) So, AB = CD and BC =DA

Slopes- Opposites are equal (same) Justifying … Part 2 Slopes- Opposites are equal (same) AB = CD and BC = DA

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. Justify M N P Justify O Task 3

Justify a Rectangle It appears to be a rectangle Need to show: Opposite sides are congruent Distance Formula Opposite sides are parallel Slopes are equal Adjacent lines form right angles Perpendicular Slopes

Justify a Rectangle Part 1 Distance Formula: prove NM OP, MP NO

Justify a Rectangle Part 2 Prove: Opposite sides are Parallel; They have the same Slopes.

Justify a Rectangle Part 3 Prove adjacent lines form right angles; Show Perpendicular slopes They are not perpendicular! Quadrilateral MNOP is not a Rectangle !

Practice

Which quadrilateral is TOCS? Justify. Task 4

Prove MATH is a trapezoid. Find the area and perimeter. Task 5

Find the equation of a line that includes an altitude of parallelogram MATH. Justify Task 8

Say What!? Write the equation of a line perpendicular. Let’s choose segment MH. Let’s use point A

Altitude Steps: Find the slope of the segment Write the perpendicular slope Use coordinate A I suggest point slope formula Simplify it into slope intercept form

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

Thus ends the Quadrilateral portion of proving shapes are what they appear to be.