# Equilateral polygons and right angles

• Apr 29th 2009, 12:16 AM
jt1894
Equilateral polygons and right angles
Help, I cannot draw this shape from its description:

1) Draw an equilateral right pentagon, with exactly 1 right angle and has at least one line of symmetry.

And I don't know how to prove this:

2) Explain why any equilateral right pentagon (i.e including the one above) cannot have more than two right angles??

• Apr 29th 2009, 10:41 PM
earboth
Quote:

Originally Posted by jt1894
Help, I cannot draw this shape from its description:

1) Draw an equilateral right pentagon, with exactly 1 right angle and has at least one line of symmetry.

...

Let a denote the length of the side.

1. Draw the axis of symmetry.
2. Draw an angle of 45° to both sides of the axis. The legs of these 2 angles are a.
3. Draw parallels at both sides of the axis of symmetry in a distance of $\displaystyle \frac12 a$.
4. Draw a circle with radius r = a from the endpoints of the legs of the 45°-legs.
5. The points of intersection of these two circles and the parallels are the two missing vertices of the pentagon.