Regular Polygons?

Geometry Level 2

True or False?

$\quad$ Statement I : If all sides of a polygon are equal, then all angles of the polygon are equal.

$\quad$ Statement II : If all angles of a polygon are equal, then all sides of the polygon are equal.

Both statements are true Only statement I is true Only statement II is true Both statements are false

1 solution

Pranshu Gaba
Jan 19, 2016

Both the statements are False .

It is possible to have a polygon with all sides equal, but not all angles equal, such as the Rhombus .

It is also possible to have a polygon with all angles equal, but not all sides equal such as the Rectangle . $_\square$

Line by line my solution is like your.

Niranjan Khanderia - 5 years, 4 months ago

good one !

Raven Herd - 5 years, 4 months ago

Those were the first shapes that came to mind when i thought of this question lol

Bryan Gonzalez - 5 years, 4 months ago

Ahh I forgot the Rhombus. You got me!

Ishan Mitra - 4 years, 6 months ago

Haha, I was using the Hexagon for reference. I tried stretching and squishing it.

Mark Angelo Valdejueza - 2 years, 8 months ago

Hexagons which have all angles equal but not all sides equal and vice versa would look something like this:

Pranshu Gaba - 2 years, 8 months ago

But some rectangles are also squares. So I think for me the correct term is a non-square rectangle?

Jayson Isidro - 5 years, 4 months ago

Some rhombus are also squares.

Vaibhav Priyadarshi - 3 years, 1 month ago