SSC (English Medium) 9th Standard - Maharashtra State Board Question Bank Solutions for Geometry

Write the following statement in conditional form.

A number having only two divisors is called a prime number.

Write the converse of the following statement.

If the sum of measures of angles in a figure is 180°, then the figure is a triangle.

Write the converse of the following statement.

If the sum of measures of two angles is 90^° then they are complement of each other.

Write the converse of the following statement.

If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

Write the converse of the following statement.

If the sum of the digits of a number is divisible by 3 then the number is divisible by 3.

Diagonals of a parallelogram `square`WXYZ intersect each other at point O. If ∠XYZ = 135° then what is the measure of ∠XWZ and ∠YZW? 

If l(OY)= 5 cm then l(WY)= ?

In the given figure, y = 108° and x = 71° Are the lines m and n parallel? Justify.

In the figure, ray AE || ray BD, ray AF is the bisector of ∠EAB and ray BC is the bisector of ∠ABD. Prove that line AF || line BC.

A transversal EF of line AB and line CD intersects the lines at point P and Q respectively. Ray PR and ray QS are parallel and bisectors ∠BPQ and ∠PQC respectively. Prove that line AB || line CD.

In the given figure, measures of some angles are shown. Using the measures find the measures of ∠x and ∠y and hence show that line l || line m.

In the given figure, if line AB || line CF and line BC || line ED then prove that ∠ABC = ∠FDE.

In the given figure, line PS is a transversal of parallel line AB and line CD. If Ray QX, ray QY, ray RX, ray RY are angle bisectors, then prove that `square` QXRY is a rectangle.

Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.

Write the antecedent (given part) and the consequent (part to be proved) in the following statement.

If all sides of a triangle are congruent then its all angles are congruent.

Write the antecedent (given part) and the consequent (part to be proved) in the following statement.

The diagonals of a parallelogram bisect each other.

Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.

Two equilateral triangles are similar.

Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.

If angles in a linear pair are congruent then each of them is a right angle.

Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.

If the altitudes drawn on two sides of a triangle are congruent then those two sides are congruent.

The length of hypotenuse of a right angled triangle is 15. Find the length of median of its hypotenuse.

In ΔPQR, ∠Q = 90°, PQ = 12, QR = 5 and QS is a median. Find l(QS).