Why easy? Because it can be solved only with elementary geometry. Why hard? Because the same reason, you have to use only elementary geometry. Hardest? You decide. Please send in solutions. See also these funny math problems.
Here is everything you need to know to solve the above problems.
Lines and Angles: When two lines intersect, opposite angles are equal and the sum of adjacent angles is 180 degrees. When two parallel lines are intersected by a third line, the corresponding angles of the two intersections are equal.
Triangles: The sum of the interior angles of a triangle is 180 degrees. An isosceles triangle has two equal sides and the two angles opposite those sides are equal. An equilateral triangle has all sides equal and all angles equal. A right triangle has one angle equal to 90 degrees. Two triangles are called similar if they have the same angles (same shape). Two triangles are called congruent if they have the same angles and the same sides (same shape and size).
- Side-Angle-Side (SAS): Two triangles are congruent if a pair of corresponding sides and the included angle are equal.
- Side-Side-Side (SSS): Two triangles are congruent if their corresponding sides are equal.
- Angle-Side-Angle (ASA): Two triangles are congruent if a pair of corresponding angles and the included side are equal.
- Angle-Angle (AA): Two triangles are similar if a pair of corresponding angles are equal.