Triangle is graphed.

1. Find the midpoint of each side of the triangle.
2. Sketch the perpendicular bisectors, using an index card to help draw 90-degree angles. Label the intersection point as .
3. Write equations for all 3 perpendicular bisectors.
4. Use the equations to find the coordinates of , and verify algebraically that the perpendicular bisectors all intersect at .

Consider triangle from an earlier activity.

1. What is the distance from to , the intersection point of the perpendicular bisectors of the triangle’s sides? Round to the nearest tenth.
2. Write the equation of a circle with center and radius .
3. Construct the circle. What do you notice?
4. Verify your hypothesis algebraically.

Consider triangle from earlier activities.

1. Plot point , the intersection point of the altitudes.
2. Plot point , the intersection point of the perpendicular bisectors.
3. Find the point where the 3 medians of the triangle intersect. Plot this point and label it .
4. What seems to be true about points and ? Prove that your observation is true.

A tessellation covers the entire plane with shapes that do not overlap or leave gaps.

1. Tile the plane with congruent rectangles:
   1. Draw the rectangles on your grid.
   2. Write the equations for lines that outline 1 rectangle.
2. Tile the plane with congruent right triangles:
   1. Draw the right triangles on your grid.
   2. Write the equations for lines that outline 1 right triangle.
3. Tile the plane with any other shapes:
   1. Draw the shapes on your grid.
   2. Write the equations for lines that outline 1 of the shapes.