I need help with these problems. ALSO, ONLY PICK THE PROPER MULTIPLE CHOICE ANSWER THAT IS ALL NOOO EXPLANATION

1. In the parallelogram, mZQRP = 21 and MZPRS = 76. Find myPQR. The diagram is not to scale. P 5 R 97 76 O 21 O 832. In parallelogram DEFG, DH = x + 2, HF = 3y, GH = 2x - 5, and HE = 3y + 3. Find the values of x and y. The diagram is not to scale. D E H G F O x = 10, y = 4 O x = 5, y = 13 O x = 4, y = 10 O x = 13, y = 53. Find the values of a and b. The diagram is not to scale. 102- 350 a = 108, b = 72 a= 145, b = 35 a = 145, b = 72 a = 108, b = 354. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain. No; you cannot prove that the quadrilateral is a parallelogram. Yes; two opposite sides are both parallel and congruent. Yes; opposite angles are congruent. Yes; both pairs of opposite sides are congruent.5. Is the line through points P(-1, -4) and Q(4, 4) perpendicular to the line through points R(-2, 2) and S(3, -6)? Explain. Yes; their slopes have product -1. O No; their slopes are not equal. No, their slopes are not opposite reciprocals. Yes; their slopes are equal.6. Which description does NOT guarantee that a quadrilateral is a parallelogram? O a quadrilateral with the diagonals bisecting each other O quadrilateral with two opposite sides parallel O a quadrilateral with both pairs of opposite sides congruent O a quadrilateral with consecutive angles supplementary7. In the coordinate plane, three vertices of rectangle MNOP are M(0, 0), N(0, c), and P(d, 0). What are the coordinates of point O? O (2d, 2c) O O ( d, c) O ( c, d)8. Find the values of the variables in the parallelogram. The diagram is not to scale. * = 31, y = 52, z = 97 * = 31, y= 52, z = 128 * = 32, y = 52, z = 128 x = 32, y = 31, Z = 979. Which two lines are parallel? I. 4y = 3x - 4 II. 4y = 5 - 3x III. 4y+ 3x = -1 O No two of the lines are parallel. O II and III O I and III O I and II11. In the figure, the horizontal lines are parallel and AB = BC= CD. Find JM. The diagram is not to scale. 13 K J D O 6 O 12 O 3 0 912. What is the equation for the line parallel to y = 4x 14 that contains P(2. 6)? O y = 4x 14 O y = 4x + 14 O y = 4x+ 2 O x = 4w 7 14 13. Lucinda wants to build a square sandbox, but she has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length. 0 Not possible; Lucinda has to be able to measure a right angle. 0 Make each diagonal the same length as four equalalength sides. 0 Arrange four equal-length sides so the diagonals are equal lengths also. 0 Arrange four equal-length sides so the diagonals bisect each other. 14. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. 61 610 Parallelogram ABCD is a rectangle, because the diagonal creates congruent angles. Parallelogram ABCD is a square, because all four angles have the same measure. Parallelogram ABCD is a rhombus, because the diagonal bisects two angles. O There is not enough information. 15. What is the equation in point-slope form for the line parallel to y = -6x + 12 that contains J(-9, 6)? O y = 6x + 60 x = 6y +60 Oy = -6x - 48 Oy = -6x - 60