Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 8 Geometry
Problem
Hint
1) The net shown folds to a cube with a missing face. Mark with an x two edges where the final square can be placed so that the net will fold to a cube with no missing faces. Start from face #1 and start folding.
  1. Face 1 folds up under face 2
  2. Face 3 folds around the side of face 2
  3. After face 3 is folded, face 4 then folds down to make a top
  4. Face 5 then folds down, making the face opposite face 2
  5. You should be able to figure out where the final square can be placed. Mark it on the figure to the left.
2) The points A(1,3), B(2,3), C(2,2), D(0,0) and the origin are the vertices of a quadrilateral. Reflect ABCD across the line y = x. Reflect the resulting image A'B'C'D across the line y = 0 to get quadrilateral A''B''C''D. What are the coordinates of A''?
  1. The only point you have to worry about is A
  2. Graph the equation y = x on the grid to the right
  3. Plot point A on the grid
  4. Reflect A around the line y = x
  5. Now reflect this new A around the x axis (y = 0)
    (This just means to negate the rotated A point's y coordinate)
  6. New A = (___,___)

Problem
Hint
3) The five pointed star shown has rotational symmetry. What is the measure of DEC?
  1. Rotational symmetry means that all angles and lengths (like DE and EC) are the same.
  2. The formula for the sum of the angles in a polygon is:
        Sum = 180(n - 1) where n is the number of sides (and angles).
  3. Our star has ____ sides.
  4. For our star, the sum is:

        sum = ______ degrees.

  5. The obtuse angle at D and C are ____ degrees
  6. There are ___ of them, totalling _____ degrees.
  7. The other acute angles sum to ____ degrees.
  8. Angle DEC (one of those small angles) = _____ degrees.
4) Two sides of a triangle have lengths of 6 inches and 11 inches. What is the range of possible values for the length of the third side, s? Express your answer using inequalities.

  1. The third side cannot be equal to or larger than the sum of the other 2 sides or it could not make a triangle.
  2. The third side must be greater than the sum of the other 2 sides or the other ends can't meet!
  3. The inequality is :
5) The figure shown is made up of horizontal segments, vertical segments and a diagonal segment. Is it possible to compute the difference in measure between angle 1 and 2? If so compute it. If not list which angle you need to know the measure of to solve the problem.
  1. Write an expression for ∠ 4 in terms of ∠ 1:

  2. Using the fact that the angles in a quadrilateral add to 360 degrees, write an expression for :
    ∠ 2 - ∠ 1: