Symmetry And Practical Geometry

(i) The rectangle has 2 lines of symmetry.

(ii) , This figure has no lines of symmetry.

(iii) In the case of an isosceles triangle. The triangle has one line of symmetry. And for an equilateral triangle, it has 3 lines of symmetry.

(iv) The circle has infinite lines of symmetry.

∴ the figure that is not symmetric with respect to any line is: (ii)

∴ the correct option is B.

As we know, that the scalene triangle has all the sides of different lengths, so, we cannot fold the triangle along any line and so, the scalene triangle cannot have any line of symmetry ie. Scalene triangle has 0 lines of symmetry.

∴ the correct option is A.

As we can fold the circle along any line along its diameters, we can say that the circle has infinite lines of symmetry.

ie. We can say that the circle has more than 4 lines of symmetry.

∴ the correct option is D.

A. M has a vertical line of symmetry.

B. H has a vertical line of symmetry.

C. E has a horizontal line of symmetry.

D. V has a vertical line of symmetry.

∴ the correct option is C.

A. X has both vertical and horizontal lines of symmetry.

B. E has only horizontal line of symmetry.

C. M has only vertical line of symmetry.

D. K has only horizontal line of symmetry.

∴ the correct option is A.

A. M has vertical line of symmetry.

B. S does not have any line of symmetry.

C. K has horizontal line of symmetry.

D. H has a vertical and a horizontal line of symmetry.

∴ the correct option is B.

A. H has 2 lines of symmetry.

B. X has 2 lines of symmetry.

C. Z has no lines of symmetry.

D. T has 1 line of symmetry.

∴ the correct option is D.

A. Ruler is used to measure the length of anything.

B. Protractor is used to measure an angle.

C. Divider is used to transfer the measured the distances.

D. Compasses are used to draw a circle.

∴ the correct option is B.

A. Ruler is used to measure the length of anything.

B. Protractor is used to measure an angle.

C. Divider is used to transfer the measured the distances.

D. Compasses are used to draw a circle.

∴ the correct option is D.

As we know that the geometry box contains 2 set squares.

∴ the correct option is C.

As we know that the ruler is in the shape of a rectangle and we know that a rectangle has 2 lines of symmetry, so we can say that the ruler has 2 lines of symmetry.

∴ the correct option is C.

As the divider is like the inverted “V”, we can say that the divider has 1 line of symmetry.

∴ the correct option is B.

As the compass is of the shape :

We can say that it does not have any line of symmetry ie. It has 0 lines of symmetry.

∴ the correct option is A.

As we know that the protractor is of the shape of the semi-circle, and as the semi circle has only one line of symmetry, so we can say that, the protractor has 1 line of symmetry.

∴ the correct option is B.

As we know that, the 45° - 45° - 90° set-square is of the shape of an isosceles triangle, and we know that the isosceles triangle has only one line of symmetry, so we can say that 45° - 45° - 90° set-square has 1 line symmetry.

∴ the correct option is B.

We can see that in the given set square all the 3 angles are different, which means that all its sides will also be different so the given set square is of the shape of the scalene triangle.

And we know that the scalene triangle does not have any lines of symmetry, so we can say that, the 30^o - 60^o - 90^o set square has 0 lines of symmetry.

∴ the correct option is A.

On observing the elements of the geometry box, we can see that only the set squares are having the shape of a triangle.

∴ the correct option is D.

Same

To make the above statement true, the word to be placed in the blank is : “same”

So, the true statement becomes :

The distance of the image of a point (or an object) from the line of symmetry (mirror) is same as that of the point (object) from the line (mirror).

one

To make the above statement true, the word to be placed in the blank is : “one”

So, the true statement becomes :

The number of lines of symmetry in a picture of Taj Mahal is one.

Equal

To make the above statement true, the word to be placed in the blank is : “equal”

So, the true statement becomes :

The number of lines of symmetry in a rectangle and a rhombus are equal.

unequal

A rectangle has two lines of symmetry and a square has four lines of symmetry.

line segment,5 cm

The reflection of any figure will be equal to the given figure.

angle, 80°

The reflection of any figure will be equal to the given figure.

line l

The reflection of the point will be on the same line if that line is the line of symmetry.

equal

If we join AB, then its line of symmetry will be its perpendicular bisector. So, P will be equidistant from both A and B, i.e., PA = PB.

five

If we draw a line of symmetry from each of the petals, we will get five such lines.

right, triangle

8, 0

They have a vertical as well as horizontal line of symmetry.

3

It has a horizontal line of symmetry.

seven

Except for 0, 3 and 8, all the other digits have no line of symmetry.

seven

The letters A, M, T, U, V, W and Y have a vertical line of symmetry.

four

The letters B, C, D and E have only a horizontal line of symmetry.

four

The letters H, I, O and X have both a vertical and horizontal line of symmetry.

ten

The letters F, G, J, L, N, R, Q, R, S and Z have no line of symmetry.

perpendicular

The perpendicular bisector of a line segment divides it into two equal parts.

six

A regular hexagon has all of sides and angles equal. So it has three lines of symmetry joining the mid-points of opposite sides and three lines of symmetry along the diagonals, joining the opposite vertices.

n

A regular polygon of n sides has all of its angles and sides equal. Thus, it will have n lines of symmetry.

It has the line of symmetry along the right angle since it angles from 0° to 180°.

zero

A 30° - 60° - 90° set-square is a scalene triangle so it will have no line of symmetry.

one

A 45° - 45° - 90° set-square is in the form of an isosceles triangle. An isosceles triangle has only one line of symmetry.

its diagonals

Each diagonal of a rhombus divides it into two equal parts (triangles).

mid-points

The lines joining the mid-points of opposite sides of a rectangle divides it into equal smaller rectangles each.

True

A right triangle can have a line of symmetry only if it is isosceles. The line of symmetry is the line joining the mid-point of the hypotenuse to the vertex of the right angle.

False

A kite has two pairs of equal adjacent sides. So it has only one line of symmetry, which is one of its diagonals such that each one of the equal sides is on its opposite sides.

True

There is no line of symmetry in a parallelogram.

False

An isosceles triangle can have only one line of symmetry. If it has more than one line of symmetry, then it has to be an equilateral triangle.

True

A rectangle has two lines of symmetry while a square has four lines of symmetry.

True

We can draw a perpendicular bisector of any line segment with a ruler and compass.

True

There can only be one mid-point of any line segment; and hence only one perpendicular bisector through that point.

False

From a point outside a line, only one perpendicular can be drawn to it. All the other lines from that point to the line will not be perpendicular.

True

Only one circle can have a given centre and radius. All other circles either have the same centre and different radius or the same radius but a different centre.

False

Using only the two set-squares, angles of 30°, 45°, 60° and 90° and their related angles can be drawn.

True

A 15° angle is the difference between a 45° angle and a 30° angle and hence can be drawn with the help of set-squares.

True

An isosceles triangle can have only one line of symmetry. If it has more than one line of symmetry, then it has to be an equilateral triangle.

False

A rectangle has two lines of symmetry while a square has four lines of symmetry.

False

The diameter of a circle is its line of symmetry. Since a circle has infinite diameters, it can have infinite lines of symmetry.

True

A 45° - 45° - 90° set-square is an isosceles right angled triangle and thus has one line of symmetry. A protractor also has only one line of symmetry along the angle of 90°.

False

Just like there can only be one bisector of a line segment, there can only be one bisector of any given angle.

False

Any regular polygon has as many lines of symmetry as the number of sides. A regular octagon has 8 sides and hence has 8 lines of symmetry.

True

A ray has infinite points on it as it is free to extend in one direction. Thus, infinitely many perpendiculars can be drawn to it, each from a point on it.