What is This Point?

Determine the properties associated with a special point inside a triangle.

Triangle in a Quadrilateral

Given the ratio of a quadrilateral’s length to width, find the ratio of the area of a special shaded region to the area of the quadrilateral.

Transforming Triangle

What is the perimeter of a rectangle formed from an equilateral triangle?

Bouncing Barney

Follow Barney’s walking pattern to determine how many times he will reach a wall before returning to his starting point.

Casting Shadows

Use a man’s shadow to determine his distance from a tree.

The Third Side

What are the possible perimeters that a given triangle can have?

All Swimmed Out

Determine the shortest path in a noncollinear route using triangles.

Optimal Triangles

Determine the largest area of a triangle given a restricted perimeter.

Equal Areas

Determine why a certain rectangle has the same area as a triangle.

Rationalize This

Find the a right triangle with rational side lengths, and a hypotenuse numerically equal to the area of the triangle.