# 8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

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1 8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral are respectively 100, 30, 92 and x. Find the value of x. Q 4 The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral. Q 5 Thee sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram. Q 6 In a triangle ABC, P,Q and R are the mid points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ. Q 7 Find the four angles P, Q, R and S in the parallelogram PQRS as shown below. Q 8 Two opposite angles of a parallelogram are (5x + 1) and (49 3x). Find the measure of these opposite angles of the parallelogram. Q 9 Prove that each of the four sides of a rhombus is of the same length. Q 10 ABCD is a rhombus. Show that diagonals AC bisects angle A as well as angle C. IX Mathematics C.B.S.E. Practice Papers Page 58

2 Q 11 In the figure given below,abcd and PQRC are rectangles and Q is the mid point of AC. Prove that PR = ½ AC. Q 12 Find the values of a and also find angles related to a as shown in the figure. Q 13 Prove that angle bisectors of a parallelogram form a rectangle. Q 14 ABC is an isosceles triangle with AB = AC and let D, F, E be the mid-points of BC, CA and AB respectively. Show that AD is perpendicular to EF and AD bisects EF. Q 15 In a triangle ABC median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram. Q 16 ABCD is parallelogram. P is a point on AD such that AP = 1/3 AD and Q is a point on BC such that CQ = 1/3 BC. Prove that AQCP is a parallelogram. IX Mathematics C.B.S.E. Practice Papers Page 59

3 Q 17 In the figure given below, triangle ABC is right angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid points of the sides AB and AC respectively, calculate the area of trapezium DECB. Q 18 ABCD is a rhombus. AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC. Q 19 In a quadrilateral ABCD, CO and DO are the bisectors of C and D respectively. Prove that. Q 20 AD is the median of ABC. E is the mid point of AD. BE produced meet AC at F. Show that AF=(1/3)AC. Q 21 Show that the quadrilateral formed by joining the mid point of the consecutive sides of a rectangle is a rhombus. Q 22 P is the mid-point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that AR = 2BC. Q 23 P,Q,R are, respectively, the mid points of sides AB, BC and CA and of a triangle ABC. PR and AQ meet at X. BR and PQ meet at Y. Prove that XY = ¼ AB. Most Important Questions Q 1 Q 2 Q 3 The sides BA and DC of a quadrilateral ABCD are produced as shown in fig. Prove that a + b = x + y. IX Mathematics C.B.S.E. Practice Papers Page 60

4 Q 4 The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. Q 5 Q 6 In a parallelogram ABCD, prove that sum of any two consecutive angles is Q 7 Q 8 In the given figure, ABCD is a parallelogram. Compute the values of x and y. IX Mathematics C.B.S.E. Practice Papers Page 61

5 Q 9 In the given figure, AN and CP are perpendicular to the diagonal BD of a parallelogram ABCD. Q 10 Q 11 In the given figure, find the four angles A, B, C and D in the parallelogram ABCD. Prove that : IX Mathematics C.B.S.E. Practice Papers Page 62

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