Numerical Practice with Quadrilaterals Topic Index | Geometry Index | Regents Exam Prep Center

 1. Which statements describe the properties of a trapezoid? a.  The bases are parallel. b.  The diagonals are congruent. c.  The opposite angles are congruent. d.  The base angles are congruent. Choose: a, b and d a, c and d a and d a only

 2. Which statements describe the properties of a rhombus? a.  The diagonals are perpendicular. b.  The diagonals are congruent. c.  The diagonals bisect each other. d.  The diagonals bisect the angles. Choose: a, b, c, and d a, c, and d a and c b and d

 3. The perimeter of a square is 80. What is the area of the square? Choose: 20 80 160 400 Explanation The sides of a square are congruent. If the perimeter is 80, each side must be 80/4 = 20.  If each side is 20, the area is base times height = 20 * 20 = 400.

 4. The diagonals of a rhombus are 10 and 24.   Find the perimeter of the rhombus. Choose: 13 40 52 48 Explanation The diagonals of a rhombus bisect each other and are perpendicular. You see 4 right triangles in the center of the rhombus with sides of 5 and 12 .  Using the Pythagorean Thm, the third side of each triangle is 13.  So the perimeter is 4(13)=52.

 5. The perimeter of a square is 24.   In simplest radical form, find the  length of the diagonal of the square. Choose: Explanation The square has 4 congruent sides. Each side must be 6. The diagonal makes two right triangles. Use the Pyth. Thm to find the diagonal.

 6. The opposite sides of a parallelogram are represented by  2x + 10  and  5x - 20.   Find the length of the side of the parallelogram represented by  4x - 1. Choose: 10 30 39 40 Explanation The opposite sides of a parallelogram are equal. 2x+10 = 5x - 20  (solve for x) x=10.  Now substitute 10 into the side you are looking to find, 4x - 1.   Answer is 40 - 1 = 39.

 7. If one angle of a parallelogram is 60 degrees, find the number of  degrees in the remaining 3 angles. Choose: 60, 60, 60 30, 60, 90 60, 120, 120 60, 120, 150 Explanation The opposite angles of a parallelogram are =. The consecutive angle are supplementary. There is one other angle of 60 and the remaining two angles are supplements of 60. (Supplementary means add to 180.)

 8. The measures of angles A and B of parallelogram ABCD are in the ratio of  2 : 7.  Find the measure of angle A. Choose: 20 40 70 140 Explanation Angles A and B are consecutive and are supp. Ratios are expressed with x's, therefore 2x + 7x = 180. Solving for x gives x = 20. Remember to find angle A.  2(20) = 40

 9. In rhombus MATH, MA = y + 8 and  AT = 4y - 7.    Find MA. Choose: 5 8 10 13 Explanation All sides of a rhombus are equal. Set y+8=4y-7  and solve for y. y= 5, but remember to solve for MA.

 10. In rectangle ABCD, the diagonals intersect at E.  If AE = 3x + y, BE = 4x - 2y, and CE = 20, find x and y. Choose: x = 3, y = 11 x = 7, y = 4 x = 7, y = -1 x = 6, y = 2 Explanation In a rectangle the diagonals are equal and bisect each other.  So all 4 sections of the diagonals =20. 3x+y=20   and    4x-2y=20 Solve these simultaneous equations. Multiple every term in 3x+y=20 by 2.  (6x+2y=40) When you add the equations, the y terms will cancel out.  This gives x = 6. Substitution gives y = 2.

 11. EF is the median (mid-segment) of trapezoid ABCD.   EF = 25 and AD = 40.  Find BC. Choose: 5 10 30 50 Explanation The median is one-half the sum of the bases. 25 = (1/2) * (x + 40) 25 = 0.5 (x + 40) 50 = x + 40 x = 10

 12. In quadrilateral PRST, the perimeter is 49.   PR = x, RS = x + 3, ST = 2x + 4, and TP = 3x.   Find the length of the shortest side of the quadrilateral. Choose: 6 7 9 18 Explanation Perimeter is the distance around the outside. A quadrilateral has 4 sides. Add all of the sides and set them equal to 49. When you solve for x, the value is 6. The side represented by x is also the smallest side.

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