English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

S is any point on side QR of a ∆PQR. Show that: PQ + QR + RP > 2PS.

D is any point on side AC of a ∆ABC with AB = AC. Show that CD < BD.

In the following figure, l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.

Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC = ∠ABC.

In the following figure, AD is the bisector of ∠BAC. Prove that AB > BD.

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in the following figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

[Hint: CN is normal to the mirror. Also, angle of incidence = angle of reflection].

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆OCD is an isosceles triangle.

AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater.

Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than `2/3` of a right angle.

Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Can all the angles of a quadrilateral be acute angles? Give reason for your answer.

Can all the angles of a quadrilateral be right angles? Give reason for your answer.

One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.

In the following figure, P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. Prove that AD = 2CD.

In the following figure, the area of parallelogram ABCD is ______.

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is ______.