Polygons & Quadrilaterals Classwork
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- Peregrine Cain
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1 Name: Class: Date: ID: A Polygons & Quadrilaterals Classwork Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The pentagon in the diagram below is formed by five rays. What is the degree measure of angle x? a. 7 c. 108 b. 96 d. 11. 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 c. octagon b. hexagon d. quadrilateral 3. 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 c. AC DB b. DEC BEA d. DE EB 4. Which statement is true about every parallelogram? a. All four sides are congruent. c. Two pairs of opposite sides are congruent. b. The interior angles are all congruent. d. The diagonals are perpendicular to each other. 5. 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. 6. A quadrilateral whose diagonals bisect each other and are perpendicular is a a. rhombus c. trapezoid b. rectangle d. parallelogram 1
2 Name: ID: A 7. Isosceles trapezoid ABCD has diagonals AC and BD. If AC = 5x + 13 and BD = 11x 5, what is the value of x? a. 8 c. 3 b d An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt. The dimensions of the rectangle are AB = 10 inches and AC = 14 inches. Find BX. a. BX = 7 inches c. BX = 5 inches b. BX = 10 inches d. BX = 14 inches 9. TRSU is a rhombus. Find SU. a. SU = 7 c. SU = 5 b. SU = 1 d. SU = In the diagram below of trapezoid RSUT, RS Ä TU, X is the midpoint of RT, and V is the midpoint of SU. If RS = 30 and XV = 44, what is the length of TU? a. 37 c. 74 b. 58 d In parallelogram STUV, SV = x + 3, VU = x 1, and TU = 4x 3. What is the length of SV? a. 5 c. 7 b. d. 4 Short Answer 1. Find, in degrees, the measures of both an interior angle and an exterior angle of a regular pentagon. Interior Angle = Exterior Angle =
3 Polygons & Quadrilaterals Classwork Answer Section MULTIPLE CHOICE 1. ANS: C. The sum of the interior angles of a pentagon is (5 )180 = 540. PTS: REF: 01103ge STA: G.G.36. ANS: D sum of interior s = sum of exterior s Ê (n )180 ˆ (n )180 = n 180 n Ë Á 180n 360 = 180n 180n n = 70 n = 4 PTS: REF: ge STA: G.G ANS: C PTS: REF: ge STA: G.G.38 TOP: Parallelograms 4. ANS: C PTS: REF: ge STA: G.G.38 TOP: Parallelograms 5. 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 6. ANS: A PTS: REF: ge STA: G.G.41 TOP: Special Quadrilaterals 7. ANS: C The diagonals of an isosceles trapezoid are congruent. 5x + 3 = 11x 5. 6x = 18 x = 3 PTS: REF: fall0801ge STA: G.G.40 TOP: Trapezoids 1
4 8. ANS: A AC = BD = 14 BX = 1 BD BX = 1 (14) = 7 A rectangle is a parallelogram. The diagonals of a parallelogram bisect each other. Substitute and simplify. A B C D Feedback Correct! The diagonals of a rectangle bisect each other. PTS: 1 DIF: Basic REF: Page 408 OBJ: Application NAT: f STA: G.G.39 TOP: 6-4 Properties of Special Parallelograms 9. ANS: A TR = RS Definition of a rhombus 5x + = x + 5 Substitute the given values. 3x = 3 Subtract x and from both sides. x = 1 Divide both sides by 3. US = TR Definition of a rhombus US = 5x + Substitute 5x + for TR. US = 5(1) + Substitute 1 for x. US = 7 Simplify. A B C D Feedback Correct! This is the value of x, not the length of segment SU. A rhombus has four congruent sides. A rhombus has four congruent sides. PTS: 1 DIF: Basic REF: Page 409 OBJ: 6-4. Using Properties of Rhombuses to Find Measures NAT: f STA: G.G.39 TOP: 6-4 Properties of Special Parallelograms 10. ANS: B The length of the midsegment of a trapezoid is the average of the lengths of its bases. x + 30 = 44. PTS: REF: ge STA: G.G.40 TOP: Trapezoids x + 30 = 88 x = 58
5 11. ANS: A Opposite sides of a parallelogram are congruent. 4x 3 = x + 3. SV = () + 3 = 5. 3x = 6 x = PTS: REF: ge STA: G.G.38 TOP: Parallelograms SHORT ANSWER 1. ANS: (5 )180 = = 108 interior = 7 exterior PTS: REF: ge STA: G.G.37 3
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