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## Monday, January 30, 2012

### Class IX Maths Assignment Area, Circles ,Constructions and Linear equations in two variables2012

Q1.  Determine the point on the graph of the linear equation x + y=6, whose ordinate is twice its abscissa.
Q2.  How many solution(s) of the equation 3x+2=2x-3 are there on the
i) Number Line            ii) Cartesian plane
Q3.  Draw the graph of the equation represented by the straight line which is parallel to the x-axis and 3 units above it.
Q4. Find the solutions of the linear equation x+2y=8, which represents a point on  i) x axis  ii) y-axis
Q5.  For what values of c, the linear equation 2x+cy=8 has equal values of x and y as its solution.
Q6. Give the geometrical interpretations of 5x+3=3x-7 as an equation
i) in one variable  ii) In two variables
Q7. Draw the graph of the equation 3x+4y=6. At what points, the graph cut the x-axis and the y-axis.
Q8. At what point does the graph of equation 2x+3y=9 meet a line which is parallel to y -axis at a distance 4 units from the origin and on the right side of the y-axis.
Q9.  P is the mid point of side BC of parallelogram ABCD such that AP bisects angle A.
Q10. Prove that bisector of any two consecutive angles of parallelogram intersect at right angles.
Q11. E and F are respectively the midpoints of non parallel sides AD and BC of trapezium. Prove that EF is parallel to AB and EF=1/2(AB+CD).
Q12.  ABCD is a rectangle in which diagonal BD bisects angle B. Show that ABCD is a Square.
Q13.  Diagonals of Quadrilateral ABCD bisect each other. If angle A = 35 degree, determine angle B.
Q14. The bisectors of angle B and angle D of quadrilateral ABCD meet CD and AB, produced at point P and Q respectively. Prove that < P+ < Q = ½(< ABC+ < ADC).
Q15. In parallelogram ABCD, AB=10cm, AD= 6cm. The bisector of angle A meets DC in A. AE and BC produced meet at F. Find the length of CF.
Q16. Evaluate: (5x+1) (x+3)-8= 5(x+1) (x+2).

Unit- Area
Q-1: Prove that the diagonals of a parallelogram divide it into four triangles of equal areas.
Q-2: Prove that triangles on the same base and between same parallels are equal in areas.
Q-3: Prove that the three straight lines joining the mid-points of the sides of a triangle divide the triangle into four triangles of equal areas.
Q-4: ABCD is trapezium with AB parallel to DC. A line parallel AC intersects AB and BC at X and Y respectively. Show that area (triangle ADX) = area (triangle ACY).
Q-5: “parallelograms on the same base and between the same parallels are equal in area.” Prove it.
Q-6: Prove that the triangles with equal areas and equal bases have equal corresponding altitudes.
Q-7: A diagonal of a parallelogram divides it into two triangles of equal areas. Prove it.
Q-8:Show that the area of a parallelogram is equal to the product of any of its sides and the corresponding altitude.
Q-9: If a triangle and a parallelogram are on the same base and between the same parallels , the area of the triangle is equal to half that of the parallelogram.
Q-10: Show that median of a triangle divides it into two triangles of equal areas.

Unit: Circle
Q-1: Two circles with centres A and B of radii 5cm and 3cm touch each other internally . If the perpendicular bisector of segment AB meets the bigger circle in P and Q , find the length of PQ.
Q-2: In a circle of radius 5cm ,AB and AC are two chords such that AB=AC=6cm . Find the length of chord BC.
Q-3: Two circles of radii 10cm and 8cm intersect and the length of the common chord is 12cm . Find the distance between their centres.
Q-4: Prove that diameter is the greatest chord in the circle.
Q-5: A,B,C and D are four points on a circle such that AB=CD. Prove that AC=BD.
Q-6: Prove that all the chords of a circle through a given point within it, the least is one which is bisected at the point.
Q-7: Two circles intersect at A and B and AC and AD are respectively the diameters of the circles. Prove that C,B and D are collinear.
Q-8: O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that Angle BOD=Angle A.
Q-9: Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side.
Q-10: “Angle subtended in the major segment is obtuse” Justify your answer
Unit: Construction
Q-1: Construct a triangle ABC with base BC=4.5cm, angle B =60o and AB+AC=7.1cm.
Q-2: Construct a triangle ABC with its perimeter=11cm and base angles of 45o and 60o.
Q-3: Construct a triangle PQR with base PQ=4.2cm , angle P=45o and PR-QR=1.4cm.
Q-4: Construct a triangle ABC with base AB=4cm , angle 45o and AC+BC=7cm.
Q-5: Construct an triangle ABC with base BC=3.5cm , angle B =60o and AB-AC=1.1cm.

Q1.  Determine the point on the graph of the linear equation x + y=6, whose ordinate is twice its abscissa.
Q2.  How many solution(s) of the equation 3x+2=2x-3 are there on the
i) Number Line            ii) Cartesian plane
Q3.  Draw the graph of the equation represented by the straight line which is parallel to the x-axis and 3 units above it.
Q4. Find the solutions of the linear equation x+2y=8, which represents a point on  i) x axis  ii) y-axis
Q5.  For what values of c, the linear equation 2x+cy=8 has equal values of x and y as its solution.
Q6. Give the geometrical interpretations of 5x+3=3x-7 as an equation
i) in one variable  ii) In two variables
Q7. Draw the graph of the equation 3x+4y=6. At what points, the graph cut the x-axis and the y-axis.
Q8. At what point does the graph of equation 2x+3y=9 meet a line which is parallel to y -axis at a distance 4 units from the origin and on the right side of the y-axis.
Q9.  P is the mid point of side BC of parallelogram ABCD such that AP bisects angle A.
Q10. Prove that bisector of any two consecutive angles of parallelogram intersect at right angles.
Q11. E and F are respectively the midpoints of non parallel sides AD and BC of trapezium. Prove that EF is parallel to AB and EF=1/2(AB+CD).
Q12.  ABCD is a rectangle in which diagonal BD bisects angle B. Show that ABCD is a Square.
Q13.  Diagonals of Quadrilateral ABCD bisect each other. If angle A = 35 degree, determine angle B.
Q14. The bisectors of angle B and angle D of quadrilateral ABCD meet CD and AB, produced at point P and Q respectively. Prove that < P+ < Q = ½(< ABC+ < ADC).
Q15. In parallelogram ABCD, AB=10cm, AD= 6cm. The bisector of angle A meets DC in A. AE and BC produced meet at F. Find the length of CF.
Q16. Evaluate: (5x+1) (x+3)-8= 5(x+1) (x+2).

Unit- Area
Q-1: Prove that the diagonals of a parallelogram divide it into four triangles of equal areas.
Q-2: Prove that triangles on the same base and between same parallels are equal in areas.
Q-3: Prove that the three straight lines joining the mid-points of the sides of a triangle divide the triangle into four triangles of equal areas.
Q-4: ABCD is trapezium with AB parallel to DC. A line parallel AC intersects AB and BC at X and Y respectively. Show that area (triangle ADX) = area (triangle ACY).
Q-5: “parallelograms on the same base and between the same parallels are equal in area.” Prove it.
Q-6: Prove that the triangles with equal areas and equal bases have equal corresponding altitudes.
Q-7: A diagonal of a parallelogram divides it into two triangles of equal areas. Prove it.
Q-8:Show that the area of a parallelogram is equal to the product of any of its sides and the corresponding altitude.
Q-9: If a triangle and a parallelogram are on the same base and between the same parallels , the area of the triangle is equal to half that of the parallelogram.
Q-10: Show that median of a triangle divides it into two triangles of equal areas.

Unit: Circle
Q-1: Two circles with centres A and B of radii 5cm and 3cm touch each other internally . If the perpendicular bisector of segment AB meets the bigger circle in P and Q , find the length of PQ.
Q-2: In a circle of radius 5cm ,AB and AC are two chords such that AB=AC=6cm . Find the length of chord BC.
Q-3: Two circles of radii 10cm and 8cm intersect and the length of the common chord is 12cm . Find the distance between their centres.
Q-4: Prove that diameter is the greatest chord in the circle.
Q-5: A,B,C and D are four points on a circle such that AB=CD. Prove that AC=BD.
Q-6: Prove that all the chords of a circle through a given point within it, the least is one which is bisected at the point.
Q-7: Two circles intersect at A and B and AC and AD are respectively the diameters of the circles. Prove that C,B and D are collinear.
Q-8: O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that Angle BOD=Angle A.
Q-9: Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side.
Q-10: “Angle subtended in the major segment is obtuse” Justify your answer
Unit: Construction
Q-1: Construct a triangle ABC with base BC=4.5cm, angle B =60o and AB+AC=7.1cm.
Q-2: Construct a triangle ABC with its perimeter=11cm and base angles of 45o and 60o.
Q-3: Construct a triangle PQR with base PQ=4.2cm , angle P=45o and PR-QR=1.4cm.
Q-4: Construct a triangle ABC with base AB=4cm , angle 45o and AC+BC=7cm.
Q-5: Construct an triangle ABC with base BC=3.5cm , angle B =60o and AB-AC=1.1cm.