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Mathematics Class 9, 27, Chapter 8: Quadrilaterals, MULTIPLE-CHOICE QUESTIONS, Choose the correct answer from the given four options in the following questions:, 1. Three angles of a quadrilateral are 60°, 86° and 110°. The fourth angle is, (a) 104°, b) 124°, (с) 94°, (d) 84° [CBSE SP 2011], 2. The value of x in the given figure is, 7x, 5x, (a) 10°, b) 20°, (с) 30°, (d) 40° [CBSE SP 2010], 3x, 3x, 3. In a quadrilateral, three angles are in the ratio 3:3:1 and, the fourth angle is 80°, then the other angles are, (a) 100°, 100°, 80°, (b) 120°, 120°, 40°, (c) 1 °,110°, 70°, 4. In a quadrilateral ABCD, AB || DC and AD = BC = 5.5 cm, and one of the angles, is 80°, then the other angles are, (d) 110°, 110°, 60°, (a) 90°, 90°, 100°, (b) 120°, 80°, 80°, (c) 80°, 100°, 100°, (d) 110°, 85°, 85°, 5. The sides of a quadrilateral are extended in order to form exterior angles., The sum of these exterior angles is, (а) 360°, (b) 270°, (c) 90°, (d) 180°, a parallelogram?, 6. Which of the following is not true for a, (a) Opposite sides are equal., (b) Opposite angles are equal., (c) Opposite angles are always bisected by the diagonals., (d) Diagonals bisect each other., 7. In a quadrilateral ABCD, if AB = BC and CD = DA, then quadrilateral ABCD, is a, (a) trapezium, (b) rhombus, (c) kite, (d) parallelogram, 8. Given a quadrilateral ABCD such that ZC = 90° and diagonal AC and BD bisect, each other at right angles, then the quadrilateral is a, (a) trapezium, (b) kite, (c) rectangle, (d) square, 9. P and Q are the mid-points of the sides AB and AC of AABC and O is any, point on side BC. O is joined to A. If S and R are the mid-points of OB and OC, respectively, then PQRS is, (a) a square, (c) a rhombus, (b) a rectangle, (d) a parallelogram
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28, Mathematics Class 9, 10. If bisectors of ZP and ZQ of a quadrilateral PQRS intersect each other at A, of, ZQ and ZR at B, of ZR and ZS at C and of ZS and ZP at D, then ABCD is a, (a) rectangle, (d) quadrilateral whose opposite angles are supplementary, (b) rhombus, (c) parallelogram, 11. ABCD is a rhombus in which ZBCD = 100°, then (x + y) equals, A, B, (a) 40°, (b) 60°, (d) 70°, (c) 80°, [CBSE SP 2011], 100°, 12. ABCD is a parallelogram. If ZA = (3x – 20)° and ZC = (x + 40)°, then the value, of x is, (a) 30, b) 40, (c) 50, d) 60, 13. D and E are the mid-points of the sides AB and AC respectively of AABC., DE is produced to F. To prove that DA is equal and parallel to FC, we need an, additional information, which is, (a) ZDAE = ZEFC, (b) AE = EF, (c) DE = F, (d) ZADE = ZECF, 14. ABCD is a parallelogram. If its diagonals are equal, then the measure of ZABC is, (a) 60°, (b) 90°, (c) 75°, 15. Diagonals AC and BD of a parallelogram ABCD intersect each other at O., If OA = 5 cm and OD = 4 cm, then the lengths of AC and BD respectively are, (d) 120°, (а) 5 ст, 4 сm, (b) 10 cm, 8 cm, (c) 2.5 cm, 2 cm, (d) 15 ст, 12 cm, 16. If the angle between two altitudes of a parallelogram through the vertex of an, obtuse angle of the parallelogram is 60°, then the angles of the parallelogram are, (a) 105°, 75°, 105°, 75°, b) 115°, 65°, 115°, 65°, (c) 120°, 60°, 120°, 60°, d) 110°, 70°, 110°, 70°, 17. In a parallelogram, if ZA = 60°, then ZD is equal to, (a) 110°, (с) 120°, b) 140°, (d) 130°, [CBSE SP 2011], 18. One angle of a quadrilateral is 114° and the remaining three angles are equal., Then, the measure of each of the three equal angles is, (a) 82°, (b) 84°, (c) 86°, (d) 9 °, 19. Given a trapezium PQRS such that PQ = 12 cm, RS, PS = QR = 8 cm. If ZR = 130°, then ZP is, (a) 130°, 5 cm, PQ || SR,, %3D, (b) 50°, (c) 15 °, (d) 12 °, 20. In parallelogram ABCD, AB = 3 cm and the diagonals AC and BD are 5.8 cm, and 4.2 cm respectively. If the diagonals AC and BD intersect at O, then the, perimeter of AAOB is, (а) 10 cm, (b) 8.8 cm, (c) 7.2 cm, (d) 8 cm
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Mathematics Class 9, 29, 21. If an angle of a parallelogram is four-fifths of its adjacent angle, then the angles, of the parallelograms are, (a) 70°, 110°, 70°, 110°, (b) 80°, 100°, 80°, 100°, (d) 60°, 120°, 60°, 120°, (c) 72°, 108°, 72°, 108°, 22. Four angles of a quadrilateral are (2x + 20)°, (3x – 30)°, (x + 10)° and (2x)°. Value, of x is, (a) 40, (b) 45, (c) 50, (d) 55, 23. ABCD is a rectangle where BC = (4x -5) cm and AD = (2x + 3) cm. Then, BC is, (а) 11 ст, (b) 12 сm, (с) 10 cm, (d) 15 cm, 24. In rhombus PQRS, PQ = 3x cm, QR = 2(x + 3) cm. Each side of the rhombus is, (а) 17 сm, (b) 19 cm, (c) 18 ст, (d) 28 cm, 25. ABCD is a rhombus in which altitude from D to side AB bisects AB. Then the, angles of the rhombus are, (a) 100°, 80°, 100°, 80°, (b) 110°, 70°, 110°, 70°, (c) 120°, 60°, 120°, 60°, (d) 130°, 50°, 130°, 50°, 26. P is the mid-point of side BC of a parallelogram ABCD such that, ZBAP = ZDAP. If AD = 10 cm, then length of CD is, (а) 10 сm, (b) 5 cm, (c) 6 сm, (d) 8 cm, 27. ABCD is a parallelogram. P and Q are respectively the mid-points of AB and, CD. PQ and diagonal AC intersect at M. If AM = 3 cm, then the length of, diagonal AC is, (а) 3 cm, (b) 4.5 cm, (c) 6 сm, (d) 7.5 cm, 28. The diagonals AC and BD of a parallelogram ABCD intersect each other at, point O. If ZBOA = 68° and ZCAD = 25°, then ZDBC is equal to, (a) 40°, (b) 43°, (c) 68°, (d) 25°, 29. In a parallelogram PQRS, PQ = 9 cm and PS = 5 cm. The bisector of ZP meets, SR in A. PA and QR produced meet at B. Then, the length of RB is, (d) 6 cт, (а) 5 cm, (b) 4 сm, (c) 9 cm, 30. M is the mid-point of side CD of a parallelogram ABCD. A line through, C parallel to MA intersects AB at P and DA produced at R. If DA = 3.5 cm,, then the length of DR is, (а) 3.5 сm, (b) 5 cm, (c) 7 cm, (d) 10.5 cm, 31. ABCD is a trapezium in which AB || DC. M and N are the mid-points of AD, and BC respectively. If AB = 12 cm, MN = 14 cm, then the length of CD is, (а) 16 ст, (b) 14 cm, (c) 12 cm, (d) 10 cm, 32. PQRS is a parallelogram. A and B are respectively the mid-points of sides, PQ and SR. AS and BQ meet the diagonal PR of length 12 cm at C and D, respectively. Then, the length of CD is, (а) 6 ст, (b) 3 ст, (c) 4 cm, (d) 5 ст
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30, Mathematics Class 9, 33. The side AB of the parallelogram ABCD is produced to X and the bisector, of ZCBX meets DA produced and DC produced at E and F respectively. If, DE=10 cm, then the length of DF is, (b) 10 cm, (а) 5 сm, (c) 7. ст, (d) 15 cm, 34. If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is, equal to, (a) 16 cm, (b) 15 cm, (c) 20 cm, (d) 17 ст, 35. In AABC, ZA = 30°, ZB = 40° and ZC = 110°. Then, the angles of the triangle, formed by joining the mid-point of the sides of this triangle are, (a) 70°, 70°, 40°, (b) 60°, 40°, 80°, (c) 30°, 40°, 110°, (d) 60°, 70°, 50°