A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Its key properties: opposite sides are equal, opposite angles are equal, adjacent angles are supplementary (add to 180°), and the diagonals bisect each other. Because the four angles sum to 360° and opposite ones are equal, knowing one angle gives all four — the opposite equals it, and each adjacent angle is 180° minus it. Rectangles, squares and rhombuses are all special parallelograms. The SAT tests these angle relationships directly and uses them as steps in larger figures, so set up “opposite equal, adjacent supplementary” whenever you see a parallelogram.
✅ Solved examples
1. In a parallelogram, one angle is 70°. Find the opposite angle.
Opposite angles are equal: 70°.
2. In a parallelogram, one angle is 70°. Find an adjacent angle.
Adjacent angles are supplementary: 180 − 70 = 110°.
3. Three angles of a quadrilateral are 80°, 100°, 80°. Find the fourth.
360 − 80 − 100 − 80 = 100°.
4. Are opposite sides of a parallelogram equal?
Yes.
✏️ Practice — try these, take hints as needed
1. In a parallelogram, one angle is 65°. Find the opposite angle.
Opposite angles are equal.
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—
65°.
2. In a parallelogram, one angle is 50°. Find an adjacent angle.
Adjacent are supplementary.
180 − 50.
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130°.
3. A parallelogram has an angle of 120°. Find the adjacent angle.
180 − 120.
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—
60°.
4. Three angles of a quadrilateral: 90°, 90°, 90°. Find the fourth.
Sum is 360°.
360 − 270.
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90°.
5. In a parallelogram the diagonals do what to each other?
They cut at their midpoints.
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—
Bisect each other.
📝 Topic test — 8 questions
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