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Unit 4 (module 2)slope,perimeter,area.notebook
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March 06, 2017
Classifying Quadrilaterals
Unit 4 (module 2)slope,perimeter,area.notebook
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Special Quadrilaterals:ParallelogramProperties:
A quadrilateral with both pairs of opposite sides parallel.Opposites sides are congruent.
Consecutive angles are supplementary
Opposite angles are congruent.
Diagonals bisect each other
(Click on each property to have it fly in for effect.)
A B
CD
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Special Quadrilaterals:RectangleProperties:
A parallelogram with four right angles.
Diagonals are congruent.
If only one right angle is marked, the figure is a rectangle.
Has all the properties of a parallelogram.
J K
LM
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:RhombusProperties:
A parallelogram with four congruent sides.
Each diagonal bisects two angles.
Diagonals are perpendicular.
All properties of a parallelogram apply.
E
F
G
H
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:TrapezoidProperties:
A quadrilateral with exactly one pair of parallel sides.
Both pairs of base angles of an isosceles trapezoid are congruent.
The base and one of the legs form the base angles.
The parallel sides are called bases; the nonparallel sides are called legs.
R S
TU
If legs are congruent, then it is an isosceles trapezoid.
Diagonals of an isosceles trapezoid are congruent.
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:SquareProperties:
A parallelogram with four congruent sides and four right angles.
Diagonals are congruent and perpendicular.
Has all the properties of a parallelogram, a rhombus and a rectangle.
Diagonals bisect opposite angles.
Diagonals bisect each other.
N O
PQ
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:KiteProperties:
A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.
Diagonals are perpendicular.
I
T
E
K
(Click on each property to have it fly in for effect.)
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Label
Name the QuadrilateralUse the eraser to reveal the name of the quadrilateral found to
the right of the figure.
Rectangle
Isosceles Trapezoid
Parallelogram
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kite
Properties of Quadrilaterals
Guess the correct answer and pop a balloon.
rhombus square trapezoid
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If you were given the coordinates of a figure and asked toclassify what type of quadrilateral it is, what might you need to know besides slope?
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March 06, 2017Pull
Pull
What is the distance formula and midpoint formula?
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Applying Distance and Midpoint Formulas
The distance d between any two points (x1, y1) and (x2, y2) in a coordinate plane is:
,(x2 y2)
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Ex. 1 Find the distance between (1, 3) and (5, 2).Let (x1, y1) = (1, 3) and (x2, y2) = (5, 2)
This means that the distance between the points is
It doesn't matter which ordered pair is and (x1, y1) (x2, y2)
units
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Ex. 1b You try:Find the distance between (3, 1) and (2, 3).
Let (x1, y1) = (3, 1) and (x2, y2) = (2, 3)
units
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Worksheet/ YOU TRY
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Sometimes you will be asked to find a missing coordinate using the distance formula.
Ex. 2 The distance between (3, 5) and (7, b) is 5 units. Find the value of b.
Plug in values and simplify
Don't forget how to square a binomial!
Combine like terms
square both sides to get rid of radical
set both sides = 0 by subtracting 25
Factor the trinomial
Apply zero product property and solve
b = 8 or b = 2
CAMBRIDGE ONLY
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Ex. 2b The distance between (4, a) and (1, 6) is 5 units. Find the value of a.
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Notice there is a comma in the formula indicating that midpoint is an ordered pair.
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Ex. 3 What is the midpoint of the line legment with endpoints (1, 2) and (3, 4)?
Fill in values and simplify
The midpoint is the ordered pair (1, 3)
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Ex. 3b What is the midpoint of the line legment with endpoints (3, 1) and (7, 5)?
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Now for let's take everything we have learned in this unitand combine it to classify quadrilaterals using slope and distance!
What do ALL quadrilaterals have in common?What must we find to compare them?
Parallelogram Rectangle Rhombus Trapezoid Square Kite
opposite sidesparallelopposite sidescongruent
opposite anglescongruent
four right angles
Diagonals congruentfour congruent sidesDiagonals perpendicularadjacent sidescongruentone pair of parallel sides
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ACT Prep Question
Which of the following is the sine of A in the right triangle below?
12 km13 km
5 km
A. 5/13 B. 5/12 C. 12/13 D. 12/5
A
BC
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Ex. 1)
How could we do this?
p. 98
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Ex. 2)
a) The diagonals are congruent
b) Is it a rectangle?
p. 109
