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P ROPERTIES OF Q UADRILATERALS

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Q UADRILATERALS Two-dimensional, closed shape Four straight sides and four angles Sum of angles: 360 ⁰ Diagonals AC, BD Line segment from one vertex to the opposite vertex Seven types of quadrilaterals

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P ARALLELOGRAM Opposite sides are parallel & equal Opposite angles are equal

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T YPES OF P ARALLELOGRAMS Parallelogram All angles are 90 ⁰ Parallelogram All angles are 90 ⁰ All sides are equal in length Rectangle SquareRhombus Parallelogram Opposite angles are equal, do not have to be 90 ⁰ All sides are equal in length

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T RAPEZOID One pair of opposite sides are parallel A “regular” trapezoid: non-parallel sides ARE equal base angles are equal Regular trapezoid

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http://www.math.com/school/subject3/lessons/S3U2L3DP.html

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O THER Q UADRILATERALS 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.

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CLICKER QUESTION #1 What is the measure of the missing angle? A. 115 ⁰ B. 45 ⁰ C. 65 ⁰ D. 125 ⁰ 115 ⁰ 65 ⁰ X 115 ⁰

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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.

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A REA OF Q UADRILATERALS Area is measured in square units Number 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 ft ² Area = 2 ft ²

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A REA OF Q UADRILATERALS Type of QuadrilateralArea Formula ParallelogramA = bh RectangleA = bh Square A = s ² RhombusA = bh TrapezoidA = (1/2)h(b1 + b2) KiteA = (1/2)(d1*d2) IrregularBreak into parts & add Key: b – base h – height s – side b1/b2 – base1/base2 d1/d2 – diagonal1/diagonal2

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E XAMPLE - F IND AREA OF QUADRILATERAL A = (1/2)h(b1 + b2) = (1/2)(4)(9 + 6) = (1/2)(60) = 30 cm ² 9cm 6cm 4cm

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CLICKER QUESTION #3 What is the area of the parallelogram? A. 50 cm ² B. 60 cm ² C. 17 cm ² D. 22 cm ²

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CLICKER QUESTION #4 The area of a rhombus is 64 in² and the base is 16 in. Find the height. A. 4 in ² B. 1024 in C. 80 in ² D. 4 in

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C OMPLETE W ORKSHEET IN P AIRS

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P AIRS #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 cm ² B. 35 cm ² C. 25 cm ² D. 20 cm ²

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P AIRS #2 The area of a square is 169 square feet. What is the length of each side? A. 42.25 ft B. 84.5 ft C. 13 ft D. 14 ft

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P AIRS #3 The area of a rectangle is 56 in² and the base is 8 in. Find the height. A. 8 in² B. 448 in C. 448 in² D. 7 in

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P AIRS #4 Find the missing angle: A. 45 ⁰ B. 65 ⁰ C. 95 ⁰ D. 115 ⁰ 115 ⁰ x

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P AIRS #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 yd ² B. 49 yd ² C. 195 yd ² D. 189 yd ² yard sandbox

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A NSWER #1 What is the measure of the missing angle? A. 115 ⁰ B. 45 ⁰ C. 65 ⁰ D. 125 ⁰ What method did you use to solve for the answer?

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A NSWER #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.

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A NSWER #3 What is the area of the parallelogram? A. 50 cm ² B. 60 cm ² C. 17 cm ² D. 22 cm ²

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A NSWER #4 The area of a rhombus is 64 in² and the base is 16 in. Find the height. A. 4 in ² B. 1024 in C. 80 in ² D. 4 in

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P AIRS – A NSWER #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 cm ² B. 35 cm ² C. 25 cm ² D. 20 cm ²

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P AIRS – A NSWER #2 The area of a square is 169 square feet. What is the length of each side? A. 42.25 ft B. 84.5 ft C. 13 ft D. 14 ft

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P AIRS – A NSWER #3 The area of a rectangle is 56 in² and the base is 8 in. Find the height. A. 8 in² B. 448 in C. 448 in² D. 7 in

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P AIRS – A NSWER #4 Find the missing angle: A. 45 ⁰ B. 65 ⁰ C. 95 ⁰ D. 115 ⁰ 115 ⁰ x

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P AIRS – A NSWER #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 yd ² B. 49 yd ² C. 195 yd ² D. 189 yd ² yard sandbox

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