Homework: Quadrilaterals & Coordinate Geometry Day 1 Wkst BIG QUIZ on Friday Warm-Up: Draw a picture of each of the following and write down as much as you can remember Trapezoid Parallelogram Rectangle Square Rhombus Kite

Properties of Quadrilaterals Trapezoid Kite Parallelogram Names Rhombus Rectangle Square

Sides Parallel Sides Trapezoid Kite 1 pair of parallel sides Parallelogram Rectangle Square Rhombus Kite 1 pair of parallel sides Sides NO parallel sides 2 pairs of parallel sides Parallel Sides 2 pairs of parallel sides 2 pairs of parallel sides. 2 pairs of parallel sides

Sides Congruent Sides Trapezoid Kite 2 pair of adjacent sides are  Parallelogram Rectangle Square Rhombus Kite Sides 2 pair of adjacent sides are  2 pair of opposite sides are  Congruent Sides AL L sides  2 pair of opposite sides are  AL L sides 

Angles Angles Trapezoid Kite One opposite pair of equal angles Parallelogram Rectangle Square Rhombus Kite Opposite angles are equal. One opposite pair of equal angles Angles Angles Opposite angles are equal. All angles are right angles (90o) All angles are right angles (90o)

Diagonals Diagonals Trapezoid Kite Parallelogram Rhombus Rectangle Square Rhombus Kite Both diagonals bisect each other One diagonal is bisected & are perpendicular Diagonals Diagonals Both diagonals bisect each other & are  Both diagonals bisect Diagonals are perpendicular Both diagonals bisect & are perpendicular

Sides, angles and diagonals Trapezoid Parallelogram Rectangle Square Rhombus Kite Sides, angles and diagonals All Three

Quadrilaterals – DRAW THIS Kite Parallelogram Trapezoid Rectangle Rhombus Isosceles Trapezoid Square

Classifying Quadrilaterals Judging by appearance, classify each quadrilateral in as many ways as possible: Square Rectangle Rhombus Parallelogram Quadrilateral Parallelogram Quadrilateral

Classifying Quadrilaterals Judging by appearance, classify each quadrilateral in as many ways as possible: Rhombus Parallelogram Quadrilateral Trapezoid Quadrilateral

Classifying Quadrilaterals Judging by appearance, classify each quadrilateral in as many ways as possible: Kite Quadrilateral Rectangle Parallelogram Quadrilateral

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) Length of the four sides: AB = CD = BC = DA =

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) Slope of the four sides: AB = CD = BC = DA = Are the sides perpendicular? (Hint: look at the slopes)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) Slope of the Diagonals: AC = BD = Are they perpendicular?

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) Length of the Diagonals: AC = BD = Point of intersection of the diagonals (Point E)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) Length of the diagonal segments: AE = BE = EC = ED =

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) CD || BA and BC || AD parallelogram

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) Length of the four sides: AB = CD = BC = DA =

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) Slope of the four sides: AB = CD = BC = DA = Are the sides perpendicular? (Hint: look at the slopes)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) Slope of the Diagonals: AC = BD = Are they perpendicular?

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) Length of the Diagonals: AC = BD = Point of intersection of the diagonals (Point E)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) Length of the Diagonals: AC = BD = Point of intersection of the diagonals (Point E)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) Length of the diagonal segments: AE = BE = EC = ED =

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2) TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU parallelogram, rectangle, rhombus, square

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. A(1, –1), B(1, –2), C(3, –3), D(3, 1) Length of the four sides: AB = CD = BC = DA =

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. A(1, –1), B(1, –2), C(3, –3), D(3, 1) Slope of the four sides: AB = CD = BC = DA = Are the sides perpendicular? (Hint: look at the slopes)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. A(1, –1), B(1, –2), C(3, –3), D(3, 1) Slope of the Diagonals: AC = BD = Are they perpendicular?

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. A(1, –1), B(1, –2), C(3, –3), D(3, 1) Length of the Diagonals: AC = BD = Point of intersection of the diagonals (Point E)

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. A(1, –1), B(1, –2), C(3, –3), D(3, 1) Length of the diagonal segments: AE = BE = EC = ED =

Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. A(1, –1), B(1, –2), C(3, –3), D(3, 1) GH || JI trapezoid

Coordinate Geometry Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.

Prove that there are 2 pairs of parallel sides Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram. Prove that there are 2 pairs of parallel sides Slope of AB. 3-(-1) = - 4 1 - 2 Slope of CD. 1 – 5 = - 4 7 – 6 Slope of BC. 5 – 3 = 2 6 - 1 5 Slope of DA. - 1 – 1 = 2 2 - 7 5

Prove that both pairs of opposite sides are congruent Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram. Prove that both pairs of opposite sides are congruent AB=√(1 – 2)2 + [3 – (- 1)2] = √17 CD=√(7 – 6)2 + (1 - 5)2 = √17 BC=√(6 – 1)2 + (5 - 3)2 = √29 DA= √(2 – 7)2 + (-1 - 1)2 = √29

Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram. Prove that the diagonals bisect each other.