Symmetry Practice Problems

Problem 1: Identify the lines of symmetry for the following shapes?

• Square
• An Equilateral triangle
• Circle

Problem 2: Determine the order of rotational symmetry for each of the following?

• A regular pentagon
• A circle

Problem 3: The following functions exhibit any symmetry? Describe the type of symmetry?

• f(x) = x²
• g(x) = cos (x)

Problem 4: Find the point of symmetry for each of the parabolas?

• y = 5x² + 10x + 2
• y = -3x² – 5x + 1

Problem 5: Determine if the quadrilateral with vertices A(1,1), B(3,5), C(7,5), and D(5,1) has any lines of symmetry.

Problem 6: Identify the order of rotational symmetry for the capital letters?

• E
• F
• k

Problem 7: Find the equations of lines of symmetry for the following geometric shapes?

• A rectangle with vertices at (0,0), (0,4), (3,4), and (3,0)
• An isosceles triangle with vertices at (0,0), (4,0), and (2,3)

Problem 8: Determine the lines of symmetry for the parallelogram with vertices at (-1,1), (3,1), (4,4), and (0,4).

Problem 9: Find the point of symmetry for each of the following curves, the graph of y = sin (x)?

Also Read,

• Real-Life Examples of Symmetry
• Symmetry

Symmetry in mathematics is a fundamental concept that refers to a kind of balance or correspondence between parts of a figure or an equation. It indicates that one part of a figure or equation is a mirror reflection, rotation, or translation of another part.

Symmetry can be found in various branches of mathematics including geometry, algebra, and even complex number theory. In this article, we are going to see a brief introduction the Symmetry and also the Solved Problems and Practice Problems on Symmetry.

There are various types of Symmetry in mathematics:

• Reflective Symmetry (Bilateral Symmetry): This occurs when a figure can be divided into two mirror-image halves by a line, which is known as the line of symmetry.

• Rotational Symmetry: A figure has rotational symmetry if it can be rotated (less than a full circle) about a central point and still look the same as it did before the rotation.

• Translational Symmetry: This type of symmetry occurs when a figure can be moved (translated) along a path in a particular direction and still appear unchanged.

• Glide Reflection Symmetry: Glide reflection symmetry combines a translation and a reflection. A figure shows glide reflection symmetry if it can be reflected across a line and then slid along the same line.

• Scaling Symmetry (Dilational Symmetry): In scaling symmetry, figures or patterns are identical in shape but different in size, often proportionally scaled versions of each other.