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Download Lesson 28: Properties of Parallelograms Part 2
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Lesson 28 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ M1 GEOMETRY Lesson 28: Properties of Parallelograms Part 2 Learning Targets 1. I can identify the properties of parallelogram, rectangles, rhombuses and squares 2. I can use the properties to solve for a missing side or a missing angle Definition: Parallelogram β A parallelogram is a quadrilateral if and only if both pairs of opposite sides are parallel. _________ ___ _________ ___ ______________________ ______________________ ______________________ _________ ___ If one pair of sides of a quadrilateral is parallel and congruent, then the quadrilateral is a parallelogram. ____________ _____________ ___ Lesson 28 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ Example 1. Decide whether the figure is a parallelogram. If yes, explain why. a) b) 6 6 Example 2. PQRS is a parallelogram. Answer the questions below. a. If PQ = 17, then SR = ____. Explain why b. If mβ R = 73°, then mβ Q = ____ and the mβ P = _____. Explain Why c. If PT = 5, then TR = ____ and PR = ____. Explain why d. If QS = 19, then ST = _____. Explain why Example 4. RSTU is a rectangle. Find the value of z. Example 5. Is this quadrilateral definitely a parallelogram? M1 GEOMETRY Lesson 28 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ Lesson 28: Properties of Parallelograms Part 2 Problem Set 1. Decide whether the quadrilateral is a parallelogram. If yes, explain your answer a. b. c. d. e. f. 2. Decide whether the quadrilateral is a parallelogram. If yes, state the theorem. a. b. c. d. e. f. M1 GEOMETRY Lesson 28 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ M1 GEOMETRY 3. Which statement is false? 1) All parallelograms are quadrilaterals. 2) All rectangles are parallelograms. 3) All squares are rhombuses. 4) All rectangles are squares. 4. The figures below is a rectangle. Find the measures of the numbered angles. Angle 1 ______________ Explain your reasoning ________________ Angle 3 ______________ Angle 4 ______________ Explain your reasoning ___________________________________ 5. The figures below are all parallelograms. Find the measures of the numbered angles. a. Find πβ 1 ________ Explain your reasoning using the properties of parallelogram________________________________________________ b. Explain why πβ 3 ππ 50° _________________________________ ___________________________________________________ c. Find the πβ 2 ____________________________________ 6. The diagram below shows parallelogram ABCD with diagonal π΄πΆ πππ πβ π· = 113 degrees and πβ πΆπ΄π· = 36 Explain why πβ π·π΄πΆ ππ 31° Lesson 28 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ GEOMETRY 7. PQRS is a parallelogram. Answer the questions below. a. If mβ Q = 126°, then mβ R = ____ and the mβ P = _____. Explain why b. If QR = 17, then SP = ____. Explain why c. If SQ = 27, then ST = ____ and TQ = ____. Explain why d. If PT = 11, then PR = _____. Explain why 8. The figures below are all parallelograms. Find the measures of the numbered angles. a. b. Angle 1 ______________ Angle 1 ______________ Explain Angle 2 ______________ Angle 3 ______________ Explain why πβ 1 ππ 140° Angle 3 ______________ M1 Lesson 28 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ 9. Period:________ Date:_________ DEFG is a rectangle. Find the values x and y M1 GEOMETRY D E 24 x2-10x (y2-9y)° G 10. DEFG is a rectangle. Find the length of Μ Μ Μ Μ DE. 11. PQRS is a rectangle. Find the value of y. F
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