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Properties of Quadrilaterals

Properties of Quadrilaterals. Quadrilaterals. 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. Parallelogram . Opposite sides are parallel & equal

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Properties of Quadrilaterals

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  1. Properties of Quadrilaterals

  2. 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

  3. Parallelogram • Opposite sides are parallel & equal • Opposite angles are equal

  4. Types of Parallelograms Rectangle Square Rhombus • Parallelogram • All angles are 90⁰ • Parallelogram • All angles are 90⁰ • All sides are equal in length • Parallelogram • Opposite angles are equal, do not have to be 90⁰ • All sides are equal in length

  5. Trapezoid • One pair of opposite sides are parallel • A “regular” trapezoid: • non-parallel sides ARE equal • base angles are equal Regular trapezoid

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

  7. 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.

  8. CLICKER QUESTION #1 • What is the measure of the missing angle? • A. 115 ⁰ • B. 45 ⁰ • C. 65 ⁰ • D. 125 ⁰ 115⁰ X 65 ⁰ 115 ⁰

  9. 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.

  10. Area of Quadrilaterals • 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 ft² • Area = 2 ft²

  11. Area of Quadrilaterals Key: b – base h – height s – side b1/b2 – base1/base2 d1/d2 – diagonal1/diagonal2

  12. Example - Find area of quadrilateral • A = (1/2)h(b1 + b2) = (1/2)(4)(9 + 6) = (1/2)(60) = 30 cm ² 6cm 4cm 9cm

  13. CLICKER QUESTION #3 • What is the area of the parallelogram? • A. 50 cm² • B. 60 cm² • C. 17 cm² • D. 22 cm²

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

  15. Complete Worksheet in Pairs

  16. 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 cm² • B. 35 cm² • C. 25 cm² • D. 20 cm²

  17. Pairs #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

  18. Pairs #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

  19. Pairs #4 • Find the missing angle: • A. 45⁰ • B. 65⁰ • C. 95⁰ • D. 115⁰ 115⁰ x

  20. 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

  21. Answer #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?

  22. 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.

  23. Answer #3 • What is the area of the parallelogram? • A. 50 cm² • B. 60 cm² • C. 17 cm² • D. 22 cm²

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

  25. 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 cm² • B. 35 cm² • C. 25 cm² • D. 20 cm²

  26. Pairs – Answer #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

  27. 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 in • C. 448 in² • D. 7 in

  28. Pairs – Answer #4 • Find the missing angle: • A. 45⁰ • B. 65⁰ • C. 95⁰ • D. 115⁰ 115⁰ x

  29. 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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