Math: Symmetry and Congruence
Identify line symmetry and compare congruent shapes
Math: Symmetry and Congruence
Identify line symmetry and compare congruent shapes
Math - Grade 4-5
- 1
A square has 4 equal sides. How many lines of symmetry does a square have?
Fold a square in different ways so both halves match exactly.
A square has 4 lines of symmetry. They are the vertical line, the horizontal line, and the 2 diagonal lines through the center. - 2
A rectangle that is not a square has how many lines of symmetry?
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. - 3
Tell whether this statement is true or false: Two shapes are congruent if they have the same shape and the same size.
Imagine placing one shape on top of the other.
This statement is true. Congruent shapes must match exactly in both shape and size. - 4
A triangle is turned clockwise but does not change size. Is it still congruent to the original triangle? Explain.
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. - 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.
Compare both the length and the width.
Yes, the two rectangles are congruent. They have the same shape and the same side lengths, so they match exactly. - 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.
No, the two squares are not congruent. They have the same shape, but they are different sizes because their side lengths are not equal. - 7
How many lines of symmetry does an equilateral triangle have?
All 3 sides and all 3 angles are equal.
An equilateral triangle has 3 lines of symmetry. Each line goes from a vertex to the midpoint of the opposite side. - 8
How many lines of symmetry does a regular hexagon have?
A regular hexagon has 6 lines of symmetry. Some lines go through opposite vertices, and some go through the midpoints of opposite sides. - 9
A shape is folded along a line, and both halves match exactly. What does this tell you about the line?
The two sides are mirror images.
This tells you that the line is a line of symmetry. A line of symmetry divides a shape into two matching halves. - 10
Shape A and Shape B are the same size and shape, but Shape B is flipped. Are the shapes congruent? Explain.
Yes, the shapes are congruent. Flipping a shape does not change its size or shape, so the two shapes still match exactly. - 11
A regular pentagon has how many lines of symmetry?
In a regular polygon, the number of symmetry lines matches the number of sides.
A regular pentagon has 5 lines of symmetry. Each line goes through one vertex and the midpoint of the opposite side. - 12
Explain the difference between symmetry and congruence.
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.