Euclidean Geometry

Q.

In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio

1. 1 : 3 : 4

2. 4 : 2 : 1

3. 4 : 4 : 1

4. 4 : 3 : 2

Q.

The lines $a^2{x}^2+bc{y}^2=a(b+c)xy$ will be coincident, if

1. $a=0$ or $b=c$

2. $a=b$ or $a=c$

3. $c=0$ or $a=b$

4. $a=b+c$

Q. The sum of angles of a triangle formed in a spherical geometry is equal to ${180}^o$.

1. True
2. False

Q.

Euclid belongs to the country

(a) India

(b) Greece

(c) Japan

(d) Egypt

Q.

Pythagoras was a student of

(a) Euclid

(b) Thales

(c) Archimedes

(d) Bhaskara

Q. If AB = x + 3, BC = 2x and AC = 4x - 5, then what will be the measure of x, if B lies on AC?

1. x = -1
2. x = -4
3. x = 10
4. x = 8

Q.

If a point C lies between two points A and B such that AC = BC, then prove that AC = AB/2. Explain by drawing the figure.

Q. The length of the diagonal of a cube is given 6√3cm , then what is the length of the edge of the cube?

Q.

The number of interwoven isosceles triangles in Sriyantra is

(a) five

(b) seven

(c) nine

(d) eleven

Q.

Who invented Geometry?

Q.

Thales belongs to the country

(a) India

(b) Egypt

(c) Greece

(d) Babylonia

Q. A plane is a flat surface, which extends indefinitely in

1. One direction only
2. Two directions only
3. Three directions only
4. All directions

Q.

In ancient India, the shapes of altars used for household rituals were

(a) squares and rectangles

(b) squares and circles

(c) triangles and rectangles

(d) trapeziums and pyramids

Q.

BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that:

​

(i) $\angle BAC+\angle OBC={90}^{\circ }$, if A is the point on the major arc

(ii) $\angle BAC-\angle OBC={90}^{\circ }$, if A is the point on the minor arc.

Q.

How to rotate a figure ${90}^{°}$ clockwise about a point?

Q. Who is the author of the book the 'Elements' ?

1. Pythagoras
2. Aryabhata
3. Euclid
4. Aristotle

Q.

The total number of propositions in the Elements are:

1. 465

2. 460

3. 13

4. 55

Q. All right angles are ___ .

Q. Euclid divided his famous treatise 'The Elements' into

1. $11$ chapters
2. $12$ chapters
3. $13$ chapters
4. $9$ chapters

Q. Prove that:

(i) $\frac{a+b+c}{a^{-1}{b}^{-1}+b^{-1}{c}^{-1}+c^{-1}{a}^{-1}}=abc$

(ii) ${\left(a^{-1}+b^{-1}\right)}^{-1}=\frac{ab}{a+b}$

Q.

In the given figure, L and M are the mid-points of AB and BC respectively.

(i) If AB=BC, prove that AL=MC.

(ii) If BL=BM, prove that AB=BC.

Q. In figure, PQRS and MNRL are rectangles. If point M is the midpoint of side PR then prove that, $\left(i\right)SL=LR,\left(ii\right)LN=\frac{1}{2}SQ.$

Q. If $a=x{y}^{p-1},b=x{y}^{q-1}\mathrm{and}c=x{y}^{r-1}$, prove that $a^{q-r}{b}^{r-p}{c}^{p-q}=1$.

Q.

What is Pythagoras theorm?

Q. Thales belongs to the country:

1. Egypt
2. Babylonia
3. India
4. Greece

Q. Observe the figure given.

Which of the following is true if PQ = RS?

1. PQ + QR = RS
2. PR = QS
3. PQ + QS = RS
4. PQ - RS = QR

Q. If thitta is an angle between the diagonals of a parallelogram ABCD whose vertices are A(0, 2) B(2, -1) C(4, 0) and D(2, 3).show that tan thitta =2

Q. 37 if ABCD is asquare then show that the points A, B, C, D are concyclic

Q. If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c².

Q. Given three distinct points in a plane, how many lines can be drawn by joining them?