English Medium Class 9 - CBSE Question Bank Solutions

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

[Hint: Use proof by contradiction].

If AB = QR, BC = PR and CA = PQ, then ______.

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if ______.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.

“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.

It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR? Why?

ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

In the following figure, if parallelogram ABCD and rectangle ABEM are of equal area, then ______.

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD ______.

An isosceles right triangle has area 8 cm². The length of its hypotenuse is ______.

The area of the isosceles triangle is `5/4 sqrt(11)` cm², if the perimeter is 11 cm and the base is 5 cm.

If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm².

The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m² is Rs 918.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m² a year. A company hired one of its walls for 6 months. How much rent did it pay?

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

Find the area of a parallelogram given in figure. Also find the length of the altitude from vertex A on the side DC.