1. Geometry Origami - Angelfish
What shape do we begin with?

2. Geometry Origami - Angelfish
Fold along the diagonal (colored side out), then unfold.
Repeat with the other diagonal.

3. Geometry Origami - Angelfish
Now fold the square in half so that you are creating a fold line that is parallel to two sides of the square. This time, fold colored side in.
Repeat, so that you have a fold line that is parallel to the other two sides of the square.

4. Geometry Origami - Angelfish
What shapes do you see?
Can you see 4 congruent squares, each made up of 2 right triangles?

5. Geometry Origami - Angelfish
Look at the square on the bottom right. Pick up the triangle on the top right of this square, and fold it so that it is on top of the other triangle in this square.

6. Geometry Origami - Angelfish
Now look at the square on the bottom left. Pick up the triangle on the top left of this square, and fold it so that it is on top of the other triangle in this square.

7. Geometry Origami - Angelfish
You should now have a right isosceles triangle.
In a right triangle, the side that is opposite of the right angle is called the hypoteneuse.

8. Geometry Origami - Angelfish
Draw a line from the right angle to the hypoteneuse so that it bisects the hypoteneuse (divides it in half).
Fold and unfold along this line.

9. Geometry Origami - Angelfish
Put a dot on the hypoteneuse about 1 cm to the left of where the fold line bisects it.
Draw a line from the right angle to the dot.

10. Geometry Origami - Angelfish
Fold the right side of the triangle (one layer) over to this second line. This new triangle becomes one of the fish fins.

11. Geometry Origami - Angelfish
Fold the left side of the triangle (one side only) over so it is on top of the first fin.

12. Geometry Origami - Angelfish
Flip the paper over and rotate so that it looks like a fish.