Unit 9: Quadrilaterals
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1 Unit 9: Quadrilaterals Topic/Assignment I CAN statement Turned in? Properties of Quadrilaterals HW: Worksheet Properties of all Quadrilaterals Properties of Parallelograms HW: Properties of Parallelograms Worksheet Proving Parallelograms HW: Proving Parallelograms Worksheet Properties of Rhombuses, Squares, and Rectangles HW: Properties of Rhombuses, Squares, and Rectangles Worksheet Properties of Kites and Trapezoids HW: Properties of Kites and Trapezoids Worksheet Special Quadrilaterals HW: Special Quadrilaterals Worksheet 1) I can find the missing angle measurements 1) I can find angle and side measures in parallelograms. 1) I can use properties to prove quadrilaterals are parallelograms. Yes No 1) I can use properties of rhombuses, rectangles and squares. 1) I can use properties of kites and trapezoids. 2) I can use the properties to find missing side and angle measures. 1) I can identify special quadrilaterals. Yes Yes Yes Yes Yes No No No No No Unit 9 Review Yes No The Unit 9 Test is on. **If all eight assignments are completed by the day the Unit 9 test is given you will receive 5 extra points on the test. **
2 Properties of Quadrilaterals 1) I can find missing angle measurements in quadrilaterals. Quadrilateral Quadrilateral Sum Find the measure of the missing angle. 1) 2) 3) Find the value of x. Then find the measure of each angle. 1) 2) 3)
3 Properties of Parallelograms Objective: To use relationships to find sides and angles in parallelograms. Definition of Parallelogram If a quadrilateral is a parallelogram Ex. 1: Sides & Angles in Parallelograms Find the missing side lengths and the missing angles in the following parallelograms. a) b) c) d) W 3n-15 X (3y + 37) 0 (6y +4) 0 27 Z 2n + 3 Y
4 Ex. 2: Diagonals of Parallelograms a) ABCD is a parallelogram. AO = 15; DB = 10. Find CO, DO, and BO. b) RSTU is a parallelogram RO =y + 3; SO = 2x; c) HIJK is a parallelogram IO = b + 2; TO = 3y 7 ; UO = x + 5. Find x and y. HO = a; KO = 3b - 10; JO = 2a 8. Find a and b.
5 Objective: Proving Parallelograms To use relationships to prove quadrilaterals are parallelograms. Ways to Prove a Quadrilateral is a Parallelogram Ex. 1 How can you show that the quadrilateral is a parallelogram? Ex. 2 For what value of x is quadrilateral CDEF a parallelogram? Ex. 3 Show that quadrilateral ABCD is a parallelogram.
6 Parallelograms Rhombuses, Rectangles, and Squares SIDES AND ANGLES: Rhombuses Rectangles Squares Venn Diagram to describe relationships PARALLELOGRAMS RHOMBUSES RECTANGLES SQUARES Ex. 1 List the quadrilaterals for which the statements are true: a) Both pairs of opposite sides are parallel. b) Both pairs of opposite sides are congruent. c) All angles are congruent. d) All sides are congruent. Ex. 2 Find the value of x: a) b) c)
7 Parallelograms DIAGONALS Rhombuses Rectangles Squares Ex. 3 List the quadrilaterals for which the statements are true. a) The diagonals are congruent. b) The diagonals bisect the angles. c) The diagonals are perpendicular
8 Kites and Trapezoids Objective: To verify and use properties of trapezoids and kites. Trapezoid If a trapezoid is isosceles Ex. 1: ABCD is an isosceles trapezoid and m B = Find m A, m C, m D. Explain how you know each angle. B C 153 o A D Ex. 2: If diagonal AC is 2x 3 and diagonal BD is 41 6x, find the value for x and the measure of each diagonal. A B D C
9 MIDSEGMENT of a Trapezoid Ex. 3: Find the midsegment or the value of x for the following trapezoids. A. B. C. D. E. F. Recall/Review Pythagorean Theorem Ex. 5: Find the missing side lengths of the following triangles. A. B. C.
10 KITE Ex. 4: Find the measures of the missing angles. A. B. C. Ex. 6: WXYZ is a kite so the diagonals are. Use the Pythagorean Theorem to find the lengths of the sides. A. B. C. 1.5
11 Unit 9 SUMMARY Special Quadrilaterals Directions: Place an X in the box for which each characteristic is true Parallelogram Rectangle Rhombus Square Kite Trapezoid Isosceles Trapezoid Figure with four sides Angles add to 360 degrees All s are Both pairs of opposite s are Only one pair of opposite s are All sides are Both pairs of opposite sides are Both pairs of opposite sides are Only one pair of opposite sides are Diagonals are Diagonals are Diagonals bisect angles at vertex Diagonals bisect each other
12 Ex. 1: Give the most specific name for the quadrilateral. Explain your reasoning. a) b) c) Ex. 2: Points P, Q, R, and S are the vertices of a quadrilateral. Give the most specific name for PQRS. Justify your answer using the distance formula, slope formula, and/or midpoint formula. 1,0, 1,2, 6,5, 3,0 P 2,1, Q 6,1, R 5,8, S 3,8 a) P Q R S b) c) P 2,7, Q 6,9, R 9,3, S 5,1 d) P 1,7, Q 5,8, R 6,2, S 2,1
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