Classifying Quadrilaterals

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1 Classifying Quadrilaterals 1

2 Special Quadrilaterals: Parallelogram A B Properties: A quadrilateral with both pairs of opposite sides parallel. Opposites sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary D C Diagonals bisect each other (Click on each property to have it fly in for effect.) 2

3 Special Quadrilaterals: Rectangle J K Properties: A parallelogram with four right angles. Has all the properties of a parallelogram. M L Diagonals are congruent. If only one right angle is marked, the figure is a rectangle. (Click on each property to have it fly in for effect.) 3

4 Special Quadrilaterals: Rhombus Properties: E A parallelogram with four congruent sides. All properties of a parallelogram apply. H F Each diagonal bisects two angles. Diagonals are perpendicular. G (Click on each property to have it fly in for effect.) 4

5 Special Quadrilaterals: Trapezoid Properties: A quadrilateral with exactly one pair of parallel sides. R S The parallel sides are called bases; the nonparallel sides are called legs. The base and one of the legs form the base angles. If legs are congruent, then it is an isosceles trapezoid. U Diagonals of an isosceles trapezoid are congruent. Both pairs of base angles of an isosceles trapezoid are congruent. T (Click on each property to have it fly in for effect.) 5

6 Special Quadrilaterals: Square N O Properties: A parallelogram with four congruent sides and four right angles. Has all the properties of a parallelogram, a rhombus and a rectangle. Diagonals are congruent and perpendicular. Q Diagonals bisect opposite angles. Diagonals bisect each other. P (Click on each property to have it fly in for effect.) 6

7 Special Quadrilaterals: Kite K Properties: A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. E I Diagonals are perpendicular. T (Click on each property to have it fly in for effect.) 7

8 Name the Quadrilateral Use the eraser to reveal the name of the quadrilateral found to the right of the figure. Rectangle Isosceles Trapezoid Parallelogram Label 8

9 Properties of Quadrilaterals Guess the correct answer and pop a balloon. rhombus square trapezoid kite 9

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11 If you were given the coordinates of a figure and asked to classify what type of quadrilateral it is, what might you need to know besides slope? 11

12 What is the distance formula and midpoint formula? Pull 12

13 Applying Distance and Midpoint Formulas The distance d between any two points (x 1, y 1 ) and (x 2, y 2 ) in a coordinate plane is: (x 2, y 2 ) 13

14 Ex. 1 Find the distance between ( 1, 3) and (5, 2). Let (x 1, y 1 ) = ( 1, 3) and (x 2, y 2 ) = (5, 2) It doesn't matter which ordered pair is (x 1, y 1 ) and (x 2, y 2 ) units This means that the distance between the points is 14

15 Ex. 1b You try: Find the distance between ( 3, 1) and (2, 3). Let (x 1, y 1 ) = ( 3, 1) and (x 2, y 2 ) = (2, 3) units 15

16 Worksheet/ YOU TRY 16

17 Sometimes you will be asked to find a missing coordinate using the distance formula. CAMBRIDGE ONLY 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 17

18 Ex. 2b The distance between (4, a) and (1, 6) is 5 units. Find the value of a. 18

19 Notice there is a comma in the formula indicating that midpoint is an ordered pair. 19

20 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) 20

21 Ex. 3b What is the midpoint of the line legment with endpoints ( 3, 1) and (7, 5)? 21

22 Now for let's take everything we have learned in this unit and combine it to classify quadrilaterals using slope and distance! What do ALL quadrilaterals have in common? What must we find to compare them? opposite sides parallel opposite sides congruent opposite angles congruent four right angles Diagonals congruent four congruent sides Diagonals perpendicular adjacent sides congruent one pair of parallel sides Parallelogram Rectangle Rhombus Trapezoid Square Kite 22

23 ACT Prep Question Which of the following is the sine of A in the right triangle below? A 13 km 12 km C 5 km B A. 5/13 B. 5/12 C. 12/13 D. 12/5 23

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26 Ex. 1) p. 98 How could we do this? 26

27 Ex. 2) p. 109 a) The diagonals are congruent b) Is it a rectangle? 27

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