The two black triangles are both equilateral, and their bases form a straight line segment. Prove that the two red lines are of equal length.

The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340 miles on the north, 515 miles on the east, 435 miles on the south and 225 miles on the west. If A and B are points located midway across the north and south boundaries, what is the approximate distance from A to B?

What is the general name of the point of concurrence for the three altitudes of a triangle?

Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.