Twice Reflected over Parallel Lines

Find an equation that relates the distance between points reflected over parallel lines.

Twice Reflected over Intersecting Lines

Find an equation which relates the angles formed by intersecting lines and points reflected over these lines.

Segments on Secant

Find an equation that relates segments on a secant.

Area of a Kite

Find an equation that relates the area of a kite to its diagonals.

Edges, Face, Vertex

Find an equation that relates the number of edges to the number of faces and the number of vertices in three-dimensional objects.

Intersecting Chords

Find an equation to relate chords of a circle.

Distance to a Point in a Rectangle

Find an equation that relates segments inside a rectangle.

Proper Patterns

Given some of the proper factors of a number, what could the number be?

Squaring Legs

Using information about how a scroboscopus squares its number of legs, can you tell how many scroboscopi Tom bought?

The Middle Digit

Investigate the pattern(s) involving the middle digit in the square of numbers whose digits are all 1’s.