# Free Introduction to Euclid's Geometry 03 Practice Test - 9th Grade

Find the measure of 2, 3 and 4 from the given figure. A.

75, 75, 105

B.

75, 85, 105

C.

105, 75, 75

D.

105, 75, 105

#### SOLUTION

Solution : D

From the figure given in the question, we can observe that

3 = 75
(Vertically opposite angles)

2 +75 = 180
(Angles on a straight line)

2 = 18075 = 105

2 = 4
(Vertically opposite angles)

4 = 105°

Match the following: A.

1-a, 2-b, 3-c

B.

1-b, 2-a, 3-c

C.

1-c, 2-b, 3-a

D.

1-b, 2-c, 3-a

#### SOLUTION

Solution : D

An angle whose measure is less than 90 is called an acute angle.
An angle whose measure is greater than 90, but less than 180 is called an obtuse angle.
An angle whose measure is 90​ is called a right angle.

Pick an option which gives the meaning of the word - Geometry.

A. Just measurement
B. Measurement of world
C. Measurement of earth
D. Measurement of anything

#### SOLUTION

Solution : C

Geometry consists of two words: Geo (meaning Earth) and Metry (or Metron meaning measurement). The meaning of geometry is 'measurement of the earth'.
In mathematical terms, geometry is the branch of mathematics where we study about different shapes and their properties. The mathematician who works in the field of geometry is called Geometer.

If QP BC, what is the measure of QAB ? A.

33

B.

y

C. x
D. x+y

#### SOLUTION

Solution : B

Since AP and BC  are parallel and considering AB as the transversal, we have:

QAB=ABC=y   [alternate angles are equal]

Aruna drew 3 lines CD, KA, TP such that:
CD = KA
CD = TP
What is the relation between KA and TP?

A. KA > TP
B. TP + KA = 2 CD
C. TP = KA
D. Data insufficient

#### SOLUTION

Solution : B and C

Euclid's axiom states that - 'Things which are equal to the same thing are equal to one another'. Hence CD = KA = TP.
Therefore,
KA + TP = CD + CD = 2 CD

Which of the following is not true about a straight line segment?

A.  A straight line segment can be drawn joining any two points.
B.  Any straight line segment can be extended indefinitely in a straight line.
C. Given any straight line segment, a circle can be drawn having the segment as diameter and any point as the centre.
D. A straight line segment is a one dimensional entity.

#### SOLUTION

Solution : C

Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as the centre is the postulate given by Euclid.
A circle cannot be drawn for any given line segment as its diameter and any point on it as the centre.

All right angles are ___  .

#### SOLUTION

Solution : Euclid in his book Elements gave 5 postulates. One of his postulates stated that:
'All right angles are congruent'.

Identify Playfair's  postulate from the following :

A. If a transversal cuts two distinct straight lines in such a way that the sum of two interior angles on the same side of the transversal is equal to 180o, then the two lines are parallel to each other.
B. If a straight line meets two other lines, so as to make the two interior angles on one side of it together less than two right angles, the other straight lines will meet if produced on that side on which the angles are less than two right angles.
C. Given a line in a plane and a point outside the line in the same plane, there is a unique line passing through the given point and parallel to the given line.
D. If a transversal cuts two parallel lines, then the sum of two interior angles on the same side of the transversal is equal to 180°.

#### SOLUTION

Solution : C

Playfair was a Scottish mathematician who's postulate is a simple equivalent version of the parallel postulate of Euclid. Playfair's postulate states that- ' Given a line in a plane and a point outside the line in the same plane, there is a unique line passing through the given point and parallel to the given line.'

AB and CD,  are straight lines. Which one of these lines is a transversal with respect to the other? A.

AB only

B.

CD only

C.

either of AB or CD

D.

neither of AB nor CD

#### SOLUTION

Solution : D

A transversal is a line which intersects two (or more) lines in two (or more) distinct points. However, in this case, either of the linesAB and CD,  intersect only in one point. Hence, neither of  AB and CD, can be a transversal.

How many theorems did Euclid give in his book - Elements?

A.

5

B.

7

C.

465

D.

1456

#### SOLUTION

Solution : C

A theorem is a proposition that has been proved logically on the basis of previously established statements. In total, see the following table: 