Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Geometry
Problem
Solution
1) A circle is enlarged by increasing its radius by 50%. What is the ratio of the area of the enlarged circle to the area of the original circle? You may express your answer as a fraction.
(Hint: you can work with any size radius.) 		Use 1 as the radius of the original circle
  1. Area of the original circle = _______________
        (leave it in terms of )

  2. Area of the enlarged circle = _________________

  3. The ratio of the larger to the smaller is:


    = _________
2) In the diagram there are two parallel line segments and a labeled line segment R that meets the line segments at a 30 degree angle. Sketch what the result is when you reflect the two parallel line segments across R. What are the measures of the new angles formed between the reflected line segments and line segment R? Imagine that R is the stem of a leaf. Hold it at both ends and rotate it 180 degrees. What does that look like?

The angle those parallel lines make with R is _______ degrees
3) Which of the following nets will correctly fold to make a triangular prism with one pointed tetrahedron side?
(Think of a pointed three sided stake.)
1. Visualize folding these flat shapes into the triangular prism with the tetrahedron end.

2. Some of them will have shapes that overlap.

3. The ones that fold correctly are _________________

Problem
Solution
4) In triangle ABC shown, AB is perpendicular to CB, and DE is parallel to AC. The angle at vertex A measures 42 degrees. What is the measure of angle DEC with the label y?
  1. If angle A is 42 degrees, the angle at C is ______degrees.

  2. If DE and AC are parallel, then triangles ABC and DBE are similar, meaning their angles are the same but their sizes are different.
  3. Therefore angle DEB is ______ degrees.

  4. DEC and DEB add to _____ degrees together, so angle DEC = _______ degrees.
5) When you translate triangle ABC 5 units east, 4 units north, 7 units west and finally 9 units south, what are the final coordinates for vertex B? Translations north and sound are displacements in the y direction.
Translations east and west are displacements in the x direction.

Add them up: the new B is
(3 + x-displacement, 3 + y-displacement) =

    (___,___)