Expert: Lynn Houston - 10/25/2010

Question
If a figure is a rectangle, is it also a square?

If a figure is a square, is it also a rectangle?

Can a right triangle be an isosceles?

Answer
no, yes and yes

Look at the definitions of square, rectangle and isosceles triangle

square: a plane rectangle with four equal sides and four right angles; a four-sided regular polygon

rectangle:  A parallelogram with four right angles

isosceles triangle:  a triangle with (at least) two equal sides

Unless the sides of the parallelogram are all equal, then it is not a square, but by definition, a square is a rectangle.

A right triangle can be an isosceles triangle if 2 sides are equal and join at a right triangle, but not all right angles are isosceles triangles.