Quadrilaterals Unit Review

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1 Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of the interior angles equal the sum of the measures of the exterior angles? a. triangle b. hexagon c. octagon d. quadrilateral. ( points) In the diagram below of regular pentagon ABCDE, EB is drawn. What is the measure of AEB? a. 36º b. 54º c. 7º d. 108º 3. ( points) In the diagram below of parallelogram ABCD with diagonals AC and BD, m 1 = 45 and m DCB = 10. What is the measure of? a. 15º b. 30º c. 45º d. 60º 1

2 Name: 4. ( points) In the diagram below, parallelogram ABCD has diagonals AC and BD that intersect at point E. Which expression is not always true? a. DAE BCE b. DEC BEA c. AC DB d. DE EB 5. ( points) In rhombus ABCD, the diagonals AC and BD intersect at E. If AE = 5 and BE = 1, what is the length of AB? a. 7 b. 10 c. 13 d ( points) Lucinda wants to build a square sandbox, but has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length. a. Arrange four equal-length sides so the diagonals bisect each other. b. Arrange four equal-length sides so the diagonals are equal lengths also. c. Make each diagonal the same length as four equal-length sides. d. Not possible; Lucinda has to be able to measure a right angle. 7. ( points) Isosceles trapezoid ABCD has diagonals AC and BD. If AC = 5x + 13 and BD = 11x 5, what is the value of x? a. 8 b c. 3 d. 1

3 Name: 8. ( points) In isosceles trapezoid ABCD, AB CD. If BC = 0, AD = 36, and AB = 17, what is the length of the altitude of the trapezoid? a. 10 b. 1 c. 15 d ( points) A quadrilateral whose diagonals bisect each other and are perpendicular is a a. rhombus b. rectangle c. trapezoid d. parallelogram 10. ( points) Two vertices of a parallelogram are A(, 3) and B(8, 11), and the intersection of the diagonals is X(7, 6). Find the coordinates of the other two vertices. a. (1, 9), (6, 1) Ê 9 b., 9 ˆ Ê, c. (11, 8), (5, 0) Ê 11 d., 11 ˆ Ê, 15, 17 ˆ 17, 19 ˆ Short Answer 11. ( points) Find, in degrees, the measures of both an interior angle and an exterior angle of a regular octagon. Interior Angle: Exterior Angle: 3

4 Name: 1. ( points) The diagram below shows isosceles trapezoid ABCD with AB Ä DC and AD BC. If m BAD = x and m BCD = 3x + 5, find m BAD. Answer: 13. (4 points) Given: Quadrilateral ABCD has vertices A( 5,6), B(6,6), C(8, 3), and D( 3, 3). Prove: Quadrilateral ABCD is a parallelogram but is neither a rhombus nor a rectangle. [The use of the grid below is optional.] 4

5 Quadrilaterals Unit Review Answer Section MULTIPLE CHOICE 1. ANS: D sum of interior s = sum of exterior s Ê (n )180 ˆ (n )180 = n 180 n 180n 360 = 180n 180n n = 70 n = 4 PTS: REF: ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons. ANS: A (n )180 A = = n (5 )180 5 = 108 AEB = PTS: REF: 0810ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 3. ANS: A DCB and ADC are supplementary adjacent angles of a parallelogram = 60. = = 15. PTS: REF: ge STA: G.G.38 TOP: Parallelograms 4. ANS: C PTS: REF: ge STA: G.G.38 TOP: Parallelograms 5. ANS: C = 13 PTS: REF: ge STA: G.G.39 TOP: Special Parallelograms 6. ANS: B PTS: DIF: L3 REF: 6-4 Special Parallelograms OBJ: 6-4. Is the Parallelogram a Rhombus or a Rectangle? NAT: NAEP 005 G3f STA: NY G.G.39 NY G.G.41 TOP: 6-4 Example 3 KEY: square reasoning Theorem 6-10 Theorem 6-11 word problem problem solving 7. ANS: C The diagonals of an isosceles trapezoid are congruent. 5x + 3 = 11x 5. = 36 6x = 18 x = 3 PTS: REF: fall0801ge STA: G.G.40 TOP: Trapezoids 1

6 8. ANS: C 36 0 = = 15 PTS: REF: ge STA: G.G.40 TOP: Trapezoids 9. ANS: A PTS: REF: ge STA: G.G.41 TOP: Special Quadrilaterals 10. ANS: A The diagonals of a parallelogram bisect each other. If the vertex opposite A is C, and the vertex opposite B is D, then X is the midpoint of AC and BD. Use the midpoint formula to find points B and D. Step 1 Solve for point C. Step Solve for point D. X = midpoint of AC X = midpoint of BD Ê X = (7,6) = + x, 3 + y ˆ Ê X = (7,6) = 8 + x, 11 + y ˆ 7 = + x, 6 = 3 + y 7 = 8 + x, 6 = 11 + y x = 1, y = 9 x = 6, y = 1 C(1, 9) D(6, 1) A B C D Feedback Correct! Use the midpoint formula and let X be the midpoint. Use the midpoint formula and let X be the midpoint. Use the midpoint formula and let X be the midpoint. PTS: DIF: Advanced REF: 1b3d9ea df-9c7d f0dea STA: NY.NYLES.MTH.05.GEO.G.G.38 NY.NYLES.MTH.05.GEO.G.G.66 NY.NYLES.MTH.05.GEO.G.G.69 LOC: MTH.C MTH.C TOP: 6-3 Conditions for Parallelograms KEY: conditions for parallelogram diagonals bisect DOK: DOK SHORT ANSWER 11. ANS: (8 )180 = = 135 interior = 45 exterior PTS: REF: ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons

7 1. ANS: 70. 3x x x + x = x + 10 = x = 350 x = 35 x = 70 PTS: REF: 08109ge STA: G.G.40 TOP: Trapezoids 13. ANS: ABÄ CD and ADÄCB because their slopes are equal. ABCD is a parallelogram because opposite side are parallel. AB BC. ABCD is not a rhombus because all sides are not equal. AB BC because their slopes are not opposite reciprocals. ABCD is not a rectangle because ABC is not a right angle. PTS: 4 REF: ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane 3

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