English Medium इयत्ता ९ - CBSE Question Bank Solutions

“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom.

Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Solve the following question using appropriate Euclid’s axiom:

Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.

Solve the following question using appropriate Euclid’s axiom:

It is known that x + y = 10 and that x = z. Show that z + y = 10?

Solve the following question using appropriate Euclid’s axiom:

Look at the figure. Show that length AH > sum of lengths of AB + BC + CD.

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have AB = BC, BX = BY. Show that AX = CY.

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have BX = `1/2` AB, BY = `1/2` BC and AB = BC. Show that BX = BY.

Solve the following question using appropriate Euclid’s axiom:

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

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.

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.