grade 9 quadrilaterals in

Class 9Quadrilaterals

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Answer the questions

(1) ABCD is a parallelogram and P and R are the midpoints of side DC and BC respectively. If line PRintersect diagonal AC at Q, prove that AC = 4CQ.

(2) ABCD is a parallelogram and the diagonals of it intersect at point O. If ‹DAO = 30 °, ‹BAO = 40 °and ‹COD = 60 °, find ‹ODC.

(3) Prove that the line segment joining the midpoints of the diagonals of a trapezium is parallel to eachof the parallel sides ans is equal to half of the difference of these sides.

(4) In a triangle ABC, AD is the median. F is the point on AC such that line BF bisect AD at E. Provethat AC = 3AF.

(5) In a rectangle ABCD, E, F, G, and H are the mid points of the four sides, what kind of shape isrepresented by EFGH.

(6) The diagonals of a parallelogram ABCD intersect at O. A line through O intersect AB at X and DCat Y. if AB = 12 cm, AD = 9 cm, and OX = 5 cm, find the length of OY.

(7) ABCD is a parallelogram. The angle bisectors of ‹A and ‹D meet at O. What is the measure of‹AOD ?

(8) In a quadrilateral ABCD, the bisectors of ∠A and ∠B intersect at P, ∠B and ∠C at Q, ∠C and ∠D at Rand ∠D and ∠A at S, what kind of a quadrilateral is PQRS.

Choose correct answer(s) from given choice

(9) ABCD is a parallelogram as shown in the figure below:

a. x < y b. x > y

c. x = y d. Can not be determined from given data

ID : in-9-Quadrilaterals [1]

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(10) In a quadrilateral PQRS, the diagonals PR and QS are equal and are perpendicular to each other.The quadrilateral PQRS is a

a. Square b. Rhombus

c. Rectangle d. All of above

(11) The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken inorder, is a rhombus if

a. PQRS is a rectangle b. Diagonals of PQRS are equal

c. Diagonals of PQRS are perpendicular d. Can not be determined

(12) The diameter of circumcircle of a rectangle is 5 cm and its breadth is 4 cm. Find it length.

a. 2.5 cm b. 16 cm

c. 1.5 cm d. 3 cm

(13) In the parallelogram PQRS, PQ = 12 cm. The altitude corresponding to the side PQ and PS are 6and 10 respectively. Find PS.

a. 7.92 cm b. 7.2 cm

c. 12 cm d. 3.6 cm

(14) The perimeter of a parallelogram is 184 cm. If one side exceeds the other side by 12 cm, what arethe sides of the parallelogram.

a. 41 cm, 53 cm b. 40 cm, 52 cm

c. 46 cm, 58 cm d. 40 cm, 28 cm

(15) In the parallellogram ABCD, find the measurement of ‹BAC and ‹DAC respectively when ‹BCA is 31° and ‹DCA is 31 °.

a. 59 °, 59 ° b. 31 °, 31 °

c. 45 °, 45 °

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Answers

(1)

(2) 80

(3)



(4)

Step 1

Following picture shows triangle ΔABC with median AD at E, and another line BF, whichbisects AD. We have also drawn another line DG which is parallel to BF

Step 2

From proportionality theorem we know that if a line is drawn parallel to one side of a triangle, itdivides other two sides in the same ration

Step 3

For triangle ΔBFC, DG is parallel to BF and using proportionality theorem we can find that,

FG

GC =

BD

DC

Step 4

Since we know that BD = DC, we can find thatGC = FG ................ (1)

Step 5

Similarly we can use proportionality theorem for triangle ΔADG,

AF

FG =

AE

ED

Step 6

But since AE = ED,FG = AF ................ (2)

Step 7

Therefore,AC = AF + FG + GCUsing relation (1) and (2),AC = AF + AF + AF,AC = 3 AF

(5) Rhombus

(6) 5 cm

(7) 90 °



(8) Quadrilateral whose opposite angles are supplementary

(9) d. Can not be determined from given data

(10) a. Square

(11) b. Diagonals of PQRS are equal

(12) d. 3 cm

(13) b. 7.2 cm

(14) b. 40 cm, 52 cm

(15) b. 31 °, 31 °



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