An Isosceles Trapezoid Problem:
Students are asked to explain why the sum of the lengths of the diagonals of an isosceles trapezoid is less than its perimeter.
Geometric Mean Proof:
Students are asked to prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.
Interior Angles of a Polygon :
Students are asked to explain why the sum of the measures of the interior angles of a convex n-gon is given by the formula (n – 2)180°.
Locating the Missing Midpoint:
Students are given a triangle in which the midpoints of two sides are shown and are asked to describe a method for locating the midpoint of the remaining side using only a straight edge and pencil.
Name That Triangle:
Students are asked to describe a triangle whose vertices are the endpoints of a segment and a point on the perpendicular bisector of a segment.
The Third Side of a Triangle:
Students are given the lengths of two sides of a triangle and asked to describe all possible lengths of the remaining side.
Triangle Proportionality Theorem:
Students are asked to prove that a line parallel to one side of a triangle divides the other two sides of the triangle proportionally.
Triangle Sum Proof:
Students are asked prove that the measures of the interior angles of a triangle sum to 180°.
Triangles and Midpoints:
Students are asked to explain why a quadrilateral formed by drawing the midsegments of a triangle is a parallelogram and to find the perimeter of the triangle formed by the midsegments.