Daily Practice Problems

Class 9 Maths

Introduction to Euclid’s Geometry

Class 9 Maths

Introduction to Euclid’s Geometry

**Question 1:**

Solve the equation a – 15 = 25 and state which axiom do you use here?

**Question 2:**

Ram and Ravi have the same weight. If they each gain weight by 2 kg, how will their new weights be compared?

**Question 3:**

If A, B and C are three points on a line, and B lies between A and C as shown in

figure, then prove that AB + BC = AC.

**Question 4:**

If a point C be the mid-point of a line segment AB, then write the relation among AC, BC and AB.

**Question 5:**

How many lines do pass through two distinct points?

**Question 6:**

In the given figure, if AB = CD, then prove that AC = BD. Also, write the Euclid’s axiom used for proving it.

**Question 7:**

Define: (a) Square (b) Perpendicular lines

**Question 8:**

In the given figure, name the following:

(i) Four collinear points

(ii) Five rays

(iii) Five line segments

(iv) Two-pairs of non-intersecting line segments.

**Question 9:**

In the given figure, AC = DC and CB = CE. Show that AB = DE. Write the Euclid’s axiom to support this.

**Question 10:**

Define each of the following terms

i. Angle ii. Line segment iii. Radius of a circle

**Question 11:**

What is Euclid’s fifth postulate?

**Question 12:**

Mohan and Sohan have the same weight. If they each gain weight by 2 kg, how will their new weights be compared?

**Question 13:**

The Euclidean geometry is valid only for figures in the _______.

**Question 14:**

Euclid’s fourth axiom says that _______.

**Question 15:**

Axioms are assumed

(a) Theorems

(b) Definitions

(c) Universal truths specific to geometry

(d) Universal truths in all branches of mathematics

**Question 16:**

Which of the following needs a proof?

(a) Definition

(b) Postulate

(c) Theorem

(d) Axiom

**Question 17:**

It is known that if x + y = 10 then x + y + z = 10 + z. Euclid’s axiom that illustrates this statement is

(a) First Axiom

(b) Second Axiom

(c) Third axiom

(d) Fourth Axiom

**Question 18:**

“Lines are parallel if they do not intersect” is stated in the form of

(a) Definition

(b) Proof

(c) Postulate

(d) Axiom

**Question 19:**

The things which are double of the same thing are

(a) equal

(b) unequal

(c) double of the same thing

(d) halves of the same thing

**Question 20:**

Which of the following statements are true?

(a) Only one line can pass through a single point.

(b) There is an infinite number of lines which pass through two distinct points.

(c) A terminated line can be produced indefinitely on both the sides

(d) If two circles are equal, then their radii are unequal.

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