A rhombus is a parallelogram with all four sides equal, but its angles are not necessarily right (if they were, it would be a square). It keeps the parallelogram angle rules — opposite angles equal, adjacent angles supplementary — and adds that its diagonals are perpendicular and bisect each other and the corner angles. A square is the special case of a rhombus with right angles. On the SAT, the most-tested facts are the equal sides and the perpendicular diagonals, plus distinguishing a rhombus from a rectangle (equal sides vs equal diagonals) and a square (which is both). Recognising which property a figure has is often the key step.
✅ Solved examples
1. Which quadrilateral has all four sides equal but not necessarily right angles?
A rhombus.
2. In a rhombus, the diagonals meet at what angle?
A right angle (they are perpendicular).
3. In a rhombus one angle is 60°. Find the opposite angle.
Opposite angles equal: 60°.
4. A rhombus with right angles is also a:
Square.
✏️ Practice — try these, take hints as needed
1. A parallelogram with four equal sides is a:
Equal sides, angles vary.
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Rhombus.
2. In a rhombus, the diagonals are:
They cross at 90°.
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Perpendicular.
3. In a rhombus one angle is 110°. Find an adjacent angle.
Adjacent are supplementary.
180 − 110.
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70°.
4. Are all four sides of a rhombus equal?
By definition.
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—
Yes.
5. A square is a special kind of rhombus with what feature?
Its angles.
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—
Right angles.
📝 Topic test — 8 questions
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