Properties that are true for ALL parallelograms
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1 Unit 5 Lesson 1 Parallelograms Essential Question: Describe the characteristics of Parallelograms. (Sides and Angles) A parallelogram is Abbreviation: Opposite Sides - Opposite Angles - Consecutive Angles - Properties that are true for ALL parallelograms Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent An angle is supplementary to both its consecutive angles Diagonals bisect each other One pair of opposite sides are congruent and parallel Example #1: Determine whether each quadrilateral is a parallelogram. Justify your answer. Example #2: If ABCD is a parallelogram, determine the following: 1. m A = 2. m D = 3. m C = 4. X = 5. CD = 6. AB =
2 Practice: Find the measures of the numbered angles for each parallelogram. 1 = 1 = 1 = 2 = 2 = 2 = 3 = 3 = 3 = Example #3: Find the coordinates of the intersection of the diagonals of HJKL with the given vertices. H(2,3) J(1, 2) K( 5, 7) and L( 4, 2) Example #4: Find the value of each variable in the following parallograms: Example #5: Find the value of each variable so that each quadrilateral is a parallelogram.
3 Unit 5 Lesson 2 Rectangles Rhombi, and Squares Essential Question: Describe the characteristics of Rectangles. (Angles, Sides, and Diagonals) Rectangle Rhombus Square Example #1: Quadrilateral QRST is a rectangle. Find the value of x and then calculate the length of each diagonal. a) QS = 4x 7 and RT = 2x + 11 b) TR = 4x 45 and SQ = x + 45 Example #2: Graph each quadrilateral with the given vertices. Determine whether the figure is a rectangle. Justify your answer using the indicated formula. a) A(4,1) B( 3,2) C(3, 1) and D( 2,4) b) X( 2,4) G(1, 2) H( 1, 3) and Y( 4,3) Distance Formula Slope Formula
4 Example #3A: Quadrilateral ABCD is a rectangle. Answer the following questions: a) If AC = 2x + 13 and DB = 4x 1, then x = and DB =. b) If m DAC = 2x + 4 and m BAC = 3x + 1, then x = and BAC =. Example #3B: Quadrilateral DKLM is a rhombus. Answer the following questions: a) If DK = 8, then KL =. b) If m KAL = 2x 8, then x =. c) If DA = 4x and AL = 5x 3, then x = and AD =. Example #4: What are the measures of the numbered angles in the rhombi? 1 = 1 = 1 = 2 = 2 = 2 = 3 = 3 = 3 = 4 = 4 = Example #5: For what value of x and/or y is the parallelogram ABCD a rhombus? a) b)
5 Unit 5 Lesson 3 Comparing Rectangles, Rhombi, and Squares Essential Question: Describe the characteristics of rhombi and squares. Compare and Contrast. Example #1: Determine if each figure is a rhombus, rectangle, or square. EXPLAIN WHY. d) e) f) Example #2: For what value of x or y is the figure given a special parallelogram? a) Square b) Rhombus c) Rectangle d) Rectangle e) Rhombus f) Rectangle
6 Example #3: Name all of the special parallelograms that have each property: A.) Diagonals are perpendicular B.) Diagonals are congruent C.) Diagonals are angle bisectors D.) Diagonals bisect each other E.) Diagonals are perpendicular bisectors of each other Example #4: Given each set of vertices, determine whether QRST or BEFG is a rhombus, rectangle, or square. List all that apply. a) b) c)
7 Unit 5 Lesson 4 Trapezoids and Kites Essential Question: Describe the characteristics of Trapezoids and Kites. Compare and Contrast. Shape and Definition Properties Illustration Example #1: CDEF is an isosceles trapezoid and m C = 65. What are m D, m E, and m F? Example #2: All of the trapezoids are isosceles trapezoids. Find the missing angle measures Q = 1 = 1 = 1 = P = 2 = 2 = 2 = S = 3 = 3 = 3 =
8 Example #3: QR is the midsegment of trapezoid LMNP. What is x? What is QR? Your Turn: EF is the midsegment of trapezoid ABCD. Calculate the value of x and the length of the midsegment. a) b) Shape and Definition Properties Illustration Example #4: Find the measure of the numbered angles in the kites below: = 1 = 1 = 4 = 1 = 4 = 2 = 2 = 2 = 5 = 2 = 5 = 3 = 3 = 3 = 3 = Example #5: Find the values of the variables in each kite. a) b)
9 Unit 6 Lesson 5 Essential Question: What can you use to classify polygons in the coordinate plane? Coordinate Geometry Example #1: A(, ) B(, ) C(, ) Length of AB Length of BC Length of AC Your Turn:
10 In order to be a rhombus, what MUST be true? Example #2: A(, ) B(, ) C(, ) D(, ) Your Turn: Your Turn: Graph and label each quadrilateral with the given vertices. Then determine the most precise name for each quadrilateral.
11 Section 6.8 Your Turn:
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