Squares, Rectangles & Parallelograms

A parallelogram has both pairs of opposite sides parallel and equal, opposite angles equal, consecutive angles supplementary (they add to 180°), and diagonals that bisect each other. A rectangle is a parallelogram with four right angles, so its diagonals are also equal in length — and each diagonal, with two sides, forms a right triangle you can solve with the Pythagorean theorem. A square is a rectangle with all four sides equal, combining every property above. These inheritance rules are the point: whatever is true of a parallelogram is automatically true of a rectangle and a square. On the GRE, don’t assume a four-sided figure is any of these unless the equal sides or right angles are marked, since the drawing is not to scale.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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