properties of quadrilaterals
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PROPERTIES OF QUADRILATERALS
QUADRILATERALS Two-dimensional,
closed shape Four straight sides
and four angles Sum of angles: 360⁰ Diagonals AC, BD
Line segment from one vertex to the opposite vertex
Seven types of quadrilaterals
PARALLELOGRAM
Opposite sides are parallel & equal
Opposite angles are equal
TYPES OF PARALLELOGRAMS
Parallelogram All angles are
90⁰
Parallelogram
All angles are 90⁰
All sides are equal in length
Rectangle Square Rhombus
Parallelogram Opposite angles
are equal, do not have to be 90⁰
All sides are equal in length
TRAPEZOID One pair of
opposite sides are parallel
A “regular” trapezoid:non-parallel sides
ARE equalbase angles are
equal
Regular trapezoid
http://www.math.com/school/subject3/lessons/S3U2L3DP.html
OTHER QUADRILATERALS Irregular quadrilaterals
No specifications Kite
Two pairs of adjacent sides are equal in length
One pair of opposite angles (the ones that are between the sides of unequal length) are equal in size.
One diagonal bisects the other. Diagonals intersect at
right angles.
CLICKER QUESTION #1
What is the measure of the missing angle?A. 115 ⁰B. 45 ⁰C. 65 ⁰D. 125 ⁰
115⁰
65 ⁰
X
115 ⁰
CLICKER QUESTION #2
Which of the following is not true?
A. The diagonals of a rhombus are congruent.
B. The diagonals of a rectangle are congruent.
C. The four sides of a rhombus are congruent.
D. The rectangle has 4 right angles.E. A rhombus is a parallelogram.
AREA OF QUADRILATERALS
Area is measured in square unitsNumber of squares required to cover the
surface
Be consistent with units Example: If a rectangle is 6 inches wide and 4
feet long, what is the area? Solution: Must convert units to make both
measurements consistent. 6 inches = ½ feet ½ ft x 4 ft = 2 ft² Area = 2 ft²
AREA OF QUADRILATERALSType of Quadrilateral Area FormulaParallelogram A = bhRectangle A = bhSquare A = s²
Rhombus A = bhTrapezoid A = (1/2)h(b1 + b2)Kite A = (1/2)(d1*d2)Irregular Break into parts & add
Key: b – base h – height s – side b1/b2 – base1/base2 d1/d2 – diagonal1/diagonal2
EXAMPLE - FIND AREA OF QUADRILATERAL
A = (1/2)h(b1 + b2) = (1/2)(4)(9 + 6)
= (1/2)(60) = 30 cm ²
9cm
6cm
4cm
CLICKER QUESTION #3 What is the area of the parallelogram?
A. 50 cm²B. 60 cm²C. 17 cm²D. 22 cm²
CLICKER QUESTION #4 The area of a rhombus is 64 in² and
the base is 16 in. Find the height.
A. 4 in²B. 1024 inC. 80 in²D. 4 in
COMPLETE WORKSHEET IN PAIRS
PAIRS #1 A quadrilateral has four sides of equal
length and the diagonals are not congruent. Each side is 5 cm in length and the distance between parallel sides is 7 cm. Determine what type of quadrilateral this is and use the corresponding formula to find the area.
A. 12 cm²B. 35 cm²C. 25 cm²D. 20 cm²
PAIRS #2 The area of a square is 169 square
feet. What is the length of each side?
A. 42.25 ftB. 84.5 ftC. 13 ftD. 14 ft
PAIRS #3 The area of a rectangle is 56 in² and
the base is 8 in. Find the height.
A. 8 in² B. 448 inC. 448 in² D. 7 in
PAIRS #4 Find the missing angle:
A. 45⁰B. 65⁰C. 95⁰D. 115⁰
115⁰
x
PAIRS #5 The Smith family has a rectangular backyard
with a base of 18 yards and a height of 11 yards. They want to put new grass in the whole backyard; however, there is a square sandbox with sides of 3 yards each in the yard. How many square yards of new grass will they need? (hint: they do not need grass to cover the sandbox) A. 55 yd² B. 49 yd² C. 195 yd² D. 189 yd²
yard
sandbox
ANSWER #1
What is the measure of the missing angle?A. 115 ⁰B. 45 ⁰C. 65 ⁰D. 125 ⁰
What method did you use to solve for the answer?
ANSWER #2
Which of the following is not true?
A. The diagonals of a rhombus are congruent.
B. The diagonals of a rectangle are congruent.
C. The four sides of a rhombus are congruent.
D. The rectangle has 4 right angles.E. A rhombus is a parallelogram.
ANSWER #3 What is the area of the parallelogram?
A. 50 cm²B. 60 cm²C. 17 cm²D. 22 cm²
ANSWER #4 The area of a rhombus is 64 in² and
the base is 16 in. Find the height.
A. 4 in²B. 1024 inC. 80 in²D. 4 in
PAIRS – ANSWER #1 A quadrilateral has four sides of equal
length and the diagonals are not congruent. Each side is 5 cm in length and the distance between parallel sides is 7 cm. Determine what type of quadrilateral this is and use the corresponding formula to find the area.
A. 12 cm²B. 35 cm²C. 25 cm²D. 20 cm²
PAIRS – ANSWER #2 The area of a square is 169 square
feet. What is the length of each side?
A. 42.25 ftB. 84.5 ftC. 13 ftD. 14 ft
PAIRS – ANSWER #3 The area of a rectangle is 56 in² and
the base is 8 in. Find the height.
A. 8 in² B. 448 inC. 448 in² D. 7 in
PAIRS – ANSWER #4 Find the missing angle:
A. 45⁰B. 65⁰C. 95⁰D. 115⁰
115⁰
x
PAIRS – ANSWER #5 The Smith family has a rectangular backyard
with a base of 18 yards and a height of 11 yards. They want to put new grass in the whole backyard; however, there is a square sandbox with sides of 3 yards each in the yard. How many square yards of new grass will they need? (hint: they do not need grass to cover the sandbox) A. 55 yd² B. 49 yd² C. 195 yd² D. 189 yd²
yard
sandbox
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