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# Maths, IX

Area of Parallelograms

1.The mid point of the sides of a triangle ABC along with any one of the vertices as the fourth

point makes a parallelogram find area .

2.ABCD is a parallelogram and X is the mid-pointof AB. If ar (AXCD) = 24 cm2, then

ar(ABC)= 24 cm2. It is true ?

1. ABC and BDE are two equilateral triangles such that D is mid-point of BC. Show that

ar (BDE) =1/4 ar (ABC).

4 If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the

parallelogram so formed will be half of that of the given quadrilateral.

1. Triangles ABC and DBC are on the same base BCwith vertices A and D on opposite sides of

BC such that ar (ABC) = ar (DBC). Show that BC bisects AD.

LINEAR EQUATION IN TWO VARIABLES

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1. Find the point at which the equation 3x – 2y = 6 meets the x-axes.

2..  Find the coordinates of the points where the line 2x y = 3 meets both the axes.

3..  Find four solutions of 2x y = 4.

4..   Give two solutions of the equation x + 3y = 8.

1. After 5 years, the age of father will be two times the age of son. Write a linear equation in two

variables to represent this statement.

1. Express y in terms of x from the equation 3x + 2y= 8 and check whether the point (4, –2) lies

on the line.

1. Two angles of a quadrilateral are 500 and 800 and other two angles are in the ratio 8:15, then find measures of the remaining two angles.
1. ABCD is a trapezium, in which ABDC and ∠A = ∠B = 45. Then find ∠C and ∠D of a trapezium
1. If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram
2. In the given figure ABCD is a rhombus, then find the value of x.
3. A square is inscribed in an isosceles right angled triangle, so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.
4. E and F respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD. Prove that   EF‖‖AB and EF = (AB + CD).
5. ABCD is a rhombus and AB is produced to E and F such that AE = AB = BF. Prove that EG and FG are perpendicular to each other.

CIRCLES

1. A circular park of radius 20 m is situated in a village. Three girls Rita, Sita and Gita are sitting at equal distance on its boundary each having a toy telephone in their hands to talk to each other. Find the length of the string of each phone
2. If two circles intersect at two points, prove that their centers lies on the perpendicular

bisector of the common chord.

1. In the given figure, if O is the centre of circle, determine ∠
2. In the given figure, A, B, C and D are points on the circle such that ∠ ACB=400 and ∠DAB= 600, then find the measure of ∠DBA
3. Find the length of a chord of a circle which is at a distance of 4 cm from the centre of the circle with radius 5 cm.
4. Prove that if chords of congruent circles subtend equal angles at their centres, then they are equal.