Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 7 Geometry

Problem
Solution
1) Trapezoid ABCD is similar to trapezoid EBFG. Find AD. Similar figures have the same shape and differ in dimensions by a scale factor.
  1. The scale factor is ______
  2. Side EG corresponds to side AD in the larger trapezoid.
  3. Apply the scale factor: AD = _____
2) In the figure, line P is parallel to line R. Angles of measures 40 degrees and 75 degrees are marked. What is the measure of angle x?
  1. When a line cuts parallel lines, the acute angles made with the parallel lines are the same, so angle A is equal to _____ degrees.
  2. A and x add to 180 degrees, so angle x = ______ degrees.

Problem
Solution
3) The points of an isosceles triangle are A=(2,3), B=(3,1), and C=(1,1). If you rotate the triangle 180 degrees about the origin and then reflect the triangle across the x-axis, what are the new coordinates for A,B, and C?
  1. Draw the points on the graph after 180 degrees rotation about the origin.


  2. Now reflect these points around the x-axis and plot them.
  3. Therefore the new coordinates are____________________
4) If a square cake with side length 8 inches serves 4 people, how many people would be able to get an equivalent serving from a 12 inch diameter circular cake? Both cakes are the same height.

  1. The area served by 1 person is _____ sq. inches

  2. The area of a 12 inch diameter circular cake = ___________

  3. The number of people this cake would serve is:____________
5) A circular cone can be created by joining the two straight edges of the shown section of a circle with central angle 90 degrees and radius 5 centimeters. What is the diameter of the created cone? (The diameter of a cone is the diameter of the circular opening where it is the widest.)
  1. The length of the quarter-circle arc =
    ___________ cm.

  2. This length is the circumference of the base of the cone, so the diameter of the cone is:
    D = __________ cm.