English Medium Class 9 - CBSE Question Bank Solutions

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have AC = DC, CB = CE. Show that AB = DE.

Solve the following question using appropriate Euclid’s axiom:

In the following figure, if OX = `1/2` XY, PX = `1/2` XZ and OX = PX, show that XY = XZ.

In the following figure AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.

In the following figure BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.

Read the following statement :

An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each.
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.

Read the following statements which are taken as axioms:

1. If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
2. If a transversal intersect two parallel lines, then alternate interior angles are equal. 

Is this system of axioms consistent? Justify your answer.

Read the following two statements which are taken as axioms:

1. If two lines intersect each other, then the vertically opposite angles are not equal.
2. If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.

Is this system of axioms consistent? Justify your answer.

Read the following axioms:

1. Things which are equal to the same thing are equal to one another.
2. If equals are added to equals, the wholes are equal.
3. Things which are double of the same thing are equal to one another.

Check whether the given system of axioms is consistent or inconsistent.

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer.

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.