• 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)