Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 5 Geometry

Problem
Hint
1) In a computer game, players get to design an amusement park. The location of each ride is marked on a coordinate grid. Jocelyn wants the four rides shown in the table to be positioned at the four corners of a rectangle. What should be the coordinates of the carousel?
Method 1: Plot the points:
1. Plot the 3 points on this grid.
2. You should be able to locate the 4th grid point on this grid. = (___,___)
Method 2:Use logic:
1. Notice that 2 of the points have the same X coordinate.
2. Notice that 2 of the points have the same Y coordinate.
3. The 4th point must have the same Y coordinate but a new X coordinate. The new point is (___,___).

2) I am a quadrilateral. I can be divided into four congruent right triangles whose side lengths are 5 cm, 12 cm, and 13 cm. Draw what I could look like and compute my area.
1. "Congruent" means all 4 right triangles are the same size and shape.
2. It really doesn't matter how you put them together to make a quadrilateral, the area will still be 4 times the area of the triangle.
3. Compute the area of the 13-12-5 triangle and multiply by 4
    area = _____
4. Draw the figure on the bottom of this page.
3) Parallelograms MLKP and PKON are congruent. The measure of angle MLK is 55o. What is the measure of angle LKP? 1. Since the parallelograms are the same, that means that angle PKO is the same as MLK.
2. Angle PKO is supplementary with angle LKP.
3. Angle LKP = _____.

Problem
Hint

4) AD and BE are two lines of symmetry for hexagon ABCDEF. Which angles must have the same measure as angle F if any? You may list angles by their vertex label.
1. With line of symmetry BE, the mirror image of angle F is _____.
2. With line of symmetry AD, the mirror image of angle F is _____.
5) An isosceles triangle has a vertex at
(3, 2) and a vertex at (7,5). The angles at these vertices are not congruent. It has a horizontal line of symmetry through the vertex at (7,5). Where is the third vertex located?
1. Plot the 2 points on the graph.
2. Draw the line of symmetry.
3. The third vertex is the reflection (mirror image) of the first point about this line.
    That point is (___,___).