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# Line of Reflections on Isosceles Triangles

Directions: How many ways can you determine the location of the line of reflection for isosceles triangle XYZ that maps Point X to Point Z?

### Hint

– What tools can you use to figure this out?
– Can you use a compass to figure this out in more than one way?
– How can you measure to find it?

We know of five ways:
– Use a compass to find the perpendicular bisector
– Use a compass to find the angle bisector
– Measure the midpoint by finding half of the length of the base by using a ruler
– Cover up the triangle by moving left to right along the base until the vertex between the congruent sides is touched.
– Trace the triangle with patty paper and fold it in half to form two congruent right triangles. Draw the line along the fold.

Source: Irvine Math Project, Nanette Johnson, and Robert Kaplinsky.

## Pythagorean Inequality

Directions: Use the whole numbers 1 through 6, at most one time each, to find …