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**Classifying Quadrilaterals**

On a Cartesian Plane

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**Classify Quadrilateral**

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

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**Rectangles Opposite sides are congruent Distance Formula**

Opposite sides are parallel Slopes Adjacent lines form right angles

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**Squares All sides are congruent Distance Formula**

Opposite sides are parallel Slope Adjacent lines form right angles Slopes

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**Rhombus All sides are congruent Distance Formula**

Opposite sides are parallel Slope

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**Parallelograms Opposite sides form parallel lines Slopes**

Opposite sides are congruent Distance Formula

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**Only one set of parallel lines**

Trapezoid Only one set of parallel lines Slope

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Practice

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**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

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**Justify It looks like a parallelogram**

Part 1 That means distance formula Opposites are the Congruent (same/equal) So, AB = CD and BC =DA

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**Slopes- Opposites are equal (same)**

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

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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

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**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

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

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**Justify a Rectangle Part 2**

Prove: Opposite sides are Parallel; They have the same Slopes.

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**Justify a Rectangle Part 3**

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

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Practice

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**Which quadrilateral is TOCS? Justify.**

Task 4

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**Prove MATH is a trapezoid. Find the area and perimeter.**

Task 5

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**Find the equation of a line that includes an altitude of parallelogram MATH.**

Justify Task 8

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**Say What!? Write the equation of a line perpendicular.**

Let’s choose segment MH. Let’s use point A

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**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

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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

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

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