Math: Symmetry and Congruence Worksheet

Question 1

A square has 4 equal sides. How many lines of symmetry does a square have?

Accepted Answer

A square has 4 lines of symmetry. They are the vertical line, the horizontal line, and the 2 diagonal lines through the center.

Question 2

A rectangle that is not a square has how many lines of symmetry?

Accepted Answer

A rectangle that is not a square has 2 lines of symmetry. One line is vertical through the center, and one line is horizontal through the center.

Question 3

Tell whether this statement is true or false: Two shapes are congruent if they have the same shape and the same size.

Accepted Answer

This statement is true. Congruent shapes must match exactly in both shape and size.

Question 4

A triangle is turned clockwise but does not change size. Is it still congruent to the original triangle? Explain.

Accepted Answer

Yes, it is still congruent to the original triangle. Turning a shape does not change its side lengths or angles, so the shape stays the same size and shape.

Question 5

Shape A is a 3-inch by 5-inch rectangle. Shape B is also a 3-inch by 5-inch rectangle. Are the two rectangles congruent? Explain.

Accepted Answer

Yes, the two rectangles are congruent. They have the same shape and the same side lengths, so they match exactly.

Question 6

Shape A is a square with side length 4 units. Shape B is a square with side length 6 units. Are the two shapes congruent? Explain.

Accepted Answer

No, the two squares are not congruent. They have the same shape, but they are different sizes because their side lengths are not equal.

Question 7

How many lines of symmetry does an equilateral triangle have?

Accepted Answer

An equilateral triangle has 3 lines of symmetry. Each line goes from a vertex to the midpoint of the opposite side.

Question 8

How many lines of symmetry does a regular hexagon have?

Accepted Answer

A regular hexagon has 6 lines of symmetry. Some lines go through opposite vertices, and some go through the midpoints of opposite sides.

Question 9

A shape is folded along a line, and both halves match exactly. What does this tell you about the line?

Accepted Answer

This tells you that the line is a line of symmetry. A line of symmetry divides a shape into two matching halves.

Question 10

Shape A and Shape B are the same size and shape, but Shape B is flipped. Are the shapes congruent? Explain.

Accepted Answer

Yes, the shapes are congruent. Flipping a shape does not change its size or shape, so the two shapes still match exactly.

Question 11

A regular pentagon has how many lines of symmetry?

Accepted Answer

A regular pentagon has 5 lines of symmetry. Each line goes through one vertex and the midpoint of the opposite side.

Question 12

Explain the difference between symmetry and congruence.

Accepted Answer

Symmetry describes a shape that can be divided into matching parts by a line. Congruence describes two shapes that have exactly the same size and shape.

Math: Symmetry and Congruence

Math: Symmetry and Congruence

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