Regents Review #13 - Quadrilateral Facts

Regents Review #13 - Quadrilateral Facts 1. Which regular polygon has a minimum rotation of 45° to carry the polygon onto itself? (A) octagon B. decagon C. hexagon D. pentagon   2. In parallelogram ABCD, diagonals AC and BD intersect at E. Which statement does not prove parallelogram ABCD is a rhombus? (A) AC ≅ DB B. AB ≅ BC C. AC ⊥ BD D. AC bisects ∠DCB   3. Quadrilateral ABCD has diagonals AC and BD. Which information is not sufficient to prove ABCD is a parallelogram? A. AC and BD bisect each other. B. AB ≅ CD and BC ≅ AD C. AB ≅ CD and AB || CD D. AB ≅ CD and BC || AD   4. The diagram below shows parallelogram LMNO with diagonal LN. m∠M = 118° and m∠LNO = 22° [Diagram of parallelogram LMNO with diagonal LN, angles M and LNO labeled] Explain why m∠NLO is 40 degrees. 5. Segment CD is the perpendicular bisector of AB at E. Which pair of segments does not have to be congruent? A. AD, BD B. AC, BC C. AE, BE D. DE, CE 6. A parallelogram must be a rectangle when its A. diagonals are perpendicular B. diagonals are congruent C. opposite sides are parallel D. opposite sides are congruent 7. A sequence of transformations maps rectangle ABCD onto rectangle A'B'C'D', as shown in the diagram below. coordinate plane with two rectangles, ABCD and A'B'C'D' Which sequence of transformations maps ABCD onto A'B'C'D' and then maps A'B'C'D' onto A''B''C''D''? (A) a reflection followed by a rotation (B) a reflection followed by a translation (C) a translation followed by a rotation (D) a translation followed by a reflection   8. In the diagram of parallelogram FRED shown below, ED is extended to A, and AF is drawn such that AF ≅ DF.   parallelogram FRED with line ED extended to point A and line segment AF drawn inside the parallelogram If m∠R = 124°, what is m∠AFD? (A) 124° (B) 112° (C) 68° (D) 56° 9. In parallelogram QRST shown below, diagonal TR is drawn, U and V are points on TS and QR, respectively, and UV intersects TR at W.   parallelogram QRST with diagonal TR, points U and V on sides TS and QR, and line segment UV intersecting TR at point W. Angles are labeled as follows: ∠S = 60°, ∠SRT = 83°, ∠TWU = 35° If m∠S = 60°, m∠SRT = 83°, and m∠TWU = 35°, what is m∠WVQ? (A) 37° (B) 60° (C) 72° (D) 83° 10. Triangle ABC and triangle DEF are graphed on the set of axes below. coordinate plane with two triangles, ABC and DEF, graphed on it Which sequence of transformations maps triangle ABC onto triangle DEF? (A) a reflection over the x-axis followed by a reflection over the y-axis (B) a 180° rotation about the origin followed by a reflection over the line y = x (C) a 90° clockwise rotation about the origin followed by a reflection over the y-axis (D) a translation 8 units to the right and 1 unit up followed by a 90° counterclockwise rotation about the origin   11. On the set of axes below, rectangle ABCD can be proven congruent to rectangle KLMN using which transformation? coordinate plane with two rectangles, ABCD and KLMN, on it. Rectangle KLMN appears to be a reflection of rectangle ABCD over the xaxis. A. rotation B. translation C. reflection over the x-axis D. reflection over the y-axis 12. Which transformation would NOT always produce an image that would be congruent to the original figure?   A. translation B. dilation C. rotation D. reflection   13. Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below. quadrilateral ABCD with diagonals AC and BD Which information is not enough to prove ABCD is a parallelogram? A. AB ≅ CD and AB ⊥ DC B. AB ≅ CD and BC ≅ DA C. AB ≅ CD and BC || AD D. AB || DC and BC || AD 14. In the diagram below, ABCD is a parallelogram, AB is extended through B to E, and CE is drawn. parallelogram ABCD with AB extended through B to point E and a line segment CE drawn from point C to point E. Angle measures are labeled: m∠D = 112° and m∠EBC = 44° If CE ≅ BE and m∠D = 112°, what is m∠E? A. 44° B. 56° C. 68° D. 112°