Symmetry

If you fold a square paper along its diagonal, do the two parts coincide?

Which of the following numbers looks the same when reflected vertically?

How many lines of symmetry are in the letter $T$?

In a symmetric figure, the left half is the _______ of the right half.

A student folds a piece of paper once and cuts out a right-angled triangle such that one of its legs (a side forming the $90^{\circ}$ angle) lies perfectly along the fold line. What is the shape of the complete cutout after the paper is unfolded?

In a $3 \times 3$ grid of squares, the square in the bottom-left corner is shaded. To make the grid symmetric about the diagonal line that connects the top-left corner to the bottom-right corner, which other square must also be shaded?

To make a symmetric design on a grid, if you color the square at row $2$, column $1$, which square must you color to make it symmetric about a central vertical line (on a $4$-column grid)?

If you fold a rectangular paper twice (once horizontally and once vertically through the midpoints) and punch a single hole in the folded corner that represents the center of the paper, how many holes will you see when you unfold it?

A square is placed inside a circle such that all its vertices touch the circle. How many lines of symmetry does this combined figure have?

In a symmetric figure, if the distance between a point $A$ and its image $A'$ is $0$, where does the point $A$ lie?

How many lines of symmetry does a rhombus (that is not a square) have?

A flower with 6 identical petals arranged evenly has how many lines of symmetry?

How many lines of symmetry does the letter '$Q$' have?

A regular dodecagon has 12 sides. How many lines of symmetry does it have?

A six-pointed star is formed by overlapping two congruent equilateral triangles such that they share the same center and point in opposite directions. How many lines of symmetry does this figure have?

A figure has line symmetry if it can be folded such that the two parts:

The number of lines of symmetry in a regular nonagon is:

A square is drawn with both its diagonals and both lines joining the midpoints of opposite sides. How many lines of symmetry does this entire network of lines have?

A rectangle has four semi-circles of equal diameter attached externally, one to each of its four sides. How many lines of symmetry does this shape have?

An equilateral triangle has a small circle placed at each of its three vertices. How many lines of symmetry does this figure have?

An analog clock shows the time $3:00$. What time will it appear to show when viewed in a vertical mirror placed to its side?

If a point is located directly on the mirror line itself, where will its reflected image be located?

A piece of paper is folded in half, and a hole is punched through both layers. When the paper is unfolded, what is the term for the fold line that separates the two identical holes?

How many lines of symmetry does a regular hexagon (a 6-sided polygon) have?

Which of these digits has both a horizontal and a vertical line of symmetry when written simply?

The letter 'S' is an example of a shape with:

How many lines of symmetry are in a regular $n$-sided polygon?

Two vertical parallel mirrors, $M_1$ and $M_2$, are placed $10\text{ cm}$ apart. A small object is placed at point $P$ between the mirrors, such that it is $3\text{ cm}$ away from mirror $M_1$. The object is first reflected in mirror $M_1$ to form an image $P_1$. Then, this image $P_1$ is reflected in mirror $M_2$ to form a final image $P_2$. What is the distance between the original point $P$ and the final image $P_2$?

How many lines of symmetry does an arrow symbol (with one head and a straight shaft) have?

In a symmetric figure, if the distance of a point from the line of symmetry is $d$, what is the distance of its image from the same line of symmetry?

How many lines of symmetry does the digit $0$ (in a perfect oval shape) have?

How many lines of symmetry does a regular polygon with $n$ sides have?

An angle with two equal arms has how many lines of symmetry?

How many lines of symmetry does a line segment have?

A plus sign symbol ($+$) with all four arms of equal length and equal thickness has how many total lines of symmetry?

How many lines of symmetry does a $30^\circ-60^\circ-90^\circ$ set square (a scalene triangular tool) have?

How many lines of symmetry does a standard heart symbol ($♡$) have?

A regular pentagon is drawn with a small identical circle centered at each of its five vertices. If one more identical circle is placed such that its center lies exactly at the midpoint of one of the pentagon's sides, how many lines of symmetry does the resulting combined figure have?

A regular polygon has lines of symmetry equal to the number of months in a year. Name the number of sides of this polygon.

How many lines of symmetry are in a figure consisting of two perpendicular lines of equal length bisecting each other?

A shape that does not look the same until it has been rotated a full $360^{\circ}$ has an order of rotational symmetry of:

What is the order of rotational symmetry for an isosceles trapezium?

What is the order of rotational symmetry of a kite shape?

A paper windmill with 4 identical wings has rotational symmetry of order:

A decorative logo has an order of rotational symmetry of $12$. Through what total angle must it be rotated about its center to match its original position for the fourth time? (Excluding the $0^\circ$ starting position).

A geometric figure has an order of rotational symmetry of $15$. How many times will it look exactly like its original position if it is rotated through a total of $120^\circ$ about its center? (Excluding the $0^\circ$ starting position).

Shape A has an angle of rotation of $60^\circ$ and Shape B has an angle of rotation of $90^\circ$. What is the smallest angle greater than $0^\circ$ at which both shapes will simultaneously match their original positions?

Which of the following has rotational symmetry of order 2 but only line symmetry of order 2?

What is the center of rotation for a regular polygon?

If a figure has an order of rotational symmetry of 2, it means the figure looks the same after a rotation of: