• 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

NamesProperties of Quadrilaterals

Trapezoid

Parallelogram

RectangleSquare

Rhombus

Kite

Sides

Trapezoid

Parallelogram

RectangleSquare

Rhombus

Kite

Parallel

Sides

1 pair of parallel sides

2 pairs of parallel sides

2 pairs of parallel sides

2 pairs of parallel sides

2 pairs of parallel sides.

NO parallel sides

Sides

Trapezoid

Parallelogram

RectangleSquare

Rhombus

Kite

Congruent

Sides

2 pair of opposite

sides are

2 pair of opposite

sides are AL L sides

AL L sides

2 pair of adjacent

sides are

Angles

Trapezoid

Parallelogram

RectangleSquare

Rhombus

Kite

Angles

All angles are right angles

(90o)All angles are right angles

(90o)

Opposite angles are

equal.

Opposite angles are

equal.

One opposite pair of equal

angles

Diagonals

Trapezoid

Parallelogram

RectangleSquare

Rhombus

Kite

Diagonals

Both diagonals bisect each

other

Both diagonals bisect each other & are

Both diagonals bisect

Diagonals are perpendicular

Both diagonals bisect & are

perpendicular

One diagonal is bisected & are perpendicular

All Three

Trapezoid

Parallelogram

RectangleSquare

Rhombus

Kite

Sides, angles and

diagonals

Quadrilaterals – DRAW THIS

Quadrilateral

Kite

Trapezoid

Rectangle

Parallelogram

Rhombus

Square

IsoscelesTrapezoid

Classifying Quadrilaterals

• Judging by appearance, classify each quadrilateral in as many ways as possible:

SquareRectangleRhombusParallelogramQuadrilateral

ParallelogramQuadrilateral

Classifying Quadrilaterals

• Judging by appearance, classify each quadrilateral in as many ways as possible:

RhombusParallelogramQuadrilateral

TrapezoidQuadrilateral

Classifying Quadrilaterals

• Judging by appearance, classify each quadrilateral in as many ways as possible:

RectangleParallelogramQuadrilateral

KiteQuadrilateral

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)

parallelogram

CD || BA and BC || AD

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the four sides:AB = CD = BC = DA =

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Slope of the four sides:AB = CD = BC = DA =

Are the sides perpendicular? (Hint: look at the slopes)

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Slope of the Diagonals:AC = BD =

Are they perpendicular?

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the Diagonals:AC = BD =

Point of intersection of the diagonals (Point E)

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the Diagonals:AC = BD =

Point of intersection of the diagonals (Point E)

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the diagonal segments:AE =BE =EC =ED =

B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)

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.

TU || SR and ST || RUTURU, RURS, RSST and STTU

C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the four sides:AB = CD = BC = DA =

C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Slope of the four sides:AB = CD = BC = DA =

Are the sides perpendicular? (Hint: look at the slopes)

C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Slope of the Diagonals:AC = BD =

Are they perpendicular?

C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the Diagonals:AC = BD =

Point of intersection of the diagonals (Point E)

C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Length of the diagonal segments:AE =BE =EC =ED =

C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)

trapezoid

Using Coordinates to Classify Quadrilaterals

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

GH || JI

Coordinate Geometry

• Show that A(2, -1),

B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.

6

4

2

-2

-4

5 10 15

D(7, 1)

C(6, 5)

B(1, 3)

A(2, -1)

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

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.

6

4

2

-2

-4

5 10 15

D(7, 1)

C(6, 5)

B(1, 3)

A(2, -1)