Symmetries are one of the most beautiful part of Geometry. Slide into reflections, rotations, translations, and more, and you'll be on your way to geometric artistry.

The lengths of the lines in the above figure (a half house) are as follows: \[\lvert \overline{AB} \rvert = 9, \lvert \overline{BC} \rvert = 3,\]\[ \lvert \overline{CD} \rvert = 3, \lvert \overline{DE} \rvert = 3, \lvert \overline{EA} \rvert = 12.\] If the shape is flipped across the line segment \(\overline{AE}\) to complete a house, what will be the perimeter of the house?

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

If rectangle \(ABCD\) in the above graph is reflected in the line \(y = -1,\) what is the image of point \(D?\) The side length of each square in the graph paper is \(1.\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

In the above diagram, shape \(B\) on the right is the reflection of shape \(A\) in the red line. Given the following numbers: \[L = 48, \quad N = 3, \quad M = 6\] in the diagram, what is the value of \(a - b + c - d?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!