**Telangana SCERT Solution Class IX (9) Math Chapter 3 The Elements of Geometry Exercise 3.1**

**(1.) (i.) How many dimensions a solid has?**

Ans. 3

**(ii.) How many books are there in Euclid’s Elements ?**

Ans. 13

**(iii.) Write the number of faces of cube and cuboid.**

Ans. Cubes and Cuboids have 6 faces.

**(iv.) What is sum of interior angles of a triangle ?**

Ans. Sum of interior angle of a triangle is 180^{0}

**(v.) Write three un-defined terms of geometry.**

Ans. The undefined terms in geometry are point, plane and line.

**(2) a) Only one line can pass through a given point.**

Ans. False.

**b) All right angles are equal.**

Ans. True.

**c) Circles with same radii are equal.**

Ans. True.

**d) A line segment can be extended on its both sides endlessly to get a straight line.**

Ans. True.

**e)** Ans. True.

**(6.) What is a conjecture ? Give an example for it.**

**Ans. **A conjecture is a statement that is believed to be tree based or observations. A conjecture might not have any formal proof.

For example: If I write a set of even number from 2 to 10 and ask someone to tell me next number he shall say 12.

2, 4, 6, 8, 10, ..

Now this is a conjecture based on observation which is believed to be true but it does not have any proof.

**(7.) Mark two points P and Q. Draw a line through P and Q. Now how many lines which are parallel to PQ, can you draw?**

**(8) In the adjacent figure, a line n falls on lines l and m such that the sum of the interior angles 1 and 2 is less than 180°, then what can you say about lines l and m.**

**(9.) In the adjacent figure, if ****∠****1 = ****∠****3, ****∠****2 = ****∠****4 and ****∠****3 = ****∠****4, write the relation between ****∠****1 and ****∠****2 using an Euclid’s postulate.**

**(10.) In the adjacent figure, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that BX = BY**

Good

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