# Free Symmetry 01 Practice Test - 7th grade

How many lines of symmetry are there in an equilateral triangle?

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#### SOLUTION

Solution :

Line of symmetry is a line which divides a figure into two equal mirror images. In an equilateral triangle, there are 3 such lines. How many lines of symmetry are there in a square?

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#### SOLUTION

Solution :

A square has 4 lines of symmetry. A regular polygon has only one line of symmetry. Say true or false.

A.

True

B.

False

#### SOLUTION

Solution : B

Every regular polygon has as many lines of symmetry as the number of its sides. So, they have multiple lines of symmetry.

The order of rotational symmetry of a square about its centre is __.

#### SOLUTION

Solution :

The order of rotational symmetry of a square about its centre is 4. The angle of rotation in a square is 90.

A shape is said to have a line symmetry when one half of it is the mirror image of the other half. True or false.

A.

True

B.

False

#### SOLUTION

Solution : B

A mirror line helps to visualise a line of symmetry, a shape has a line of symmetry when half of it is the mirror image of the other half. But it is not applicable in the case of left-right changes in the orientation.
eg. R | Я
When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry. Line AB is a line of symmetry. True or False.

A.

True

B.

False

#### SOLUTION

Solution : B

Diagonal of a rectangle divides the rectangle into two triangles that are congruent, but folding along the line AB does not make the two triangles coincide with each other.

Hence AB is not a line of symmetry.

A regular hexagon's order of  rotational symmetry is seven. (True/False)

A.

True

B.

False

#### SOLUTION

Solution : B

A regular hexagon's order of  rotational symmetry is six.

Step 1: Order of rotational symmetry depends upon the number of equal sides that a regular polygon has.
Step 2: The given figure has 6 equal sides.
Step 3: So, it has rotational symmetry of order 6.

In a regular hexagon each internal angle measures 108. (True or False)

A.

True

B.

False

#### SOLUTION

Solution : B

Internal angle of regular polygon =  (n2)×180n
where, n is the number of sides.

Substituting, n = 6 in the above formula, we get internal angle as 120 for a regular hexagon.

Consider a regular pentagon. Mark the centre of pentagon as O. Centre of pentagon is defined as a point which is equidistant from all the vertices. Hence, if a vertical line is drawn through O, perpendicular to the plane in which pentagon is drawn, then the vertical line is called as line of symmetry. State true or false.

A.

True

B.

False

#### SOLUTION

Solution : B

If a vertical line is drawn through O, perpendicular to the plane in which pentagon is drawn, then the vertical line is called axis of symmetry. Hence, the given statement is false.

Which of the following figures has/have more than one line of symmetry?

(i)   Square
(ii)  Rectangle
(iii) Regular pentagon
(iv) Isosceles triangle

A.

Only (i)

B.

Only (i) and (ii)

C.

Only (i), (ii) and (iii)

D.

(i), (ii) and (iv)

#### SOLUTION

Solution : C

A square has 4 lines of symmetry. A rectangle has 2 lines of symmetry. A regular pentagon has 5 lines of symmetry. An isosceles triangle has only one line of symmetry. Thus, the figures with more than one line of symmetry are: square, rectangle and regular pentagon.