- Opposite Sides – non-consecutive sides.
- Not side-by-side
- The opposite sides of a parallelogram are congruent because the opposite sides are parallel
- Determining if a Polygon is a Parallelogram
- When you are asked, “Is this a parallelogram?”
- You should choose “possibly” if:
- You don’t have enough information to prove it is a parallelogram.
- None of the information you have proves that it is not a parallelogram.
- Do NOT choose “True” unless you are 100% certain that it’s ALWAYS true.
- Choose “False” if you are not 100% certain.
- If something is “possible,” choose “False” because possible truths are not ALWAYS true.
- If something is “True” sometimes, choose “False” because it is NOT true ALL the time!
- If BOTH pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram
- If BOTH pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram
- If ONE pair of opposite sides is BOTH parallel AND congruent, then it is a parallelogram
- Test it out for yourself! Click here!
- If BOTH pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram
- If ALL pairs of consecutive angles are supplementary (add up to 180°), then it is a parallelogram
- If BOTH diagonals bisect each other, then it is a parallelogram
- Special Cases
- If you have one pair of congruent sides AND one pair of congruent opposite angles, you can prove the quadrilateral is a parallelogram.
- If you have one pair of congruent sides AND the SAME pair of parallel sides, you can prove the quadrilateral is a parallelogram.
- If you have one pair of parallel sides AND one pair of alternate interior angles, you can prove the quadrilateral is a parallelogram (based on the proof in the video).
- In the “Test” tables (below), only ONE of the “if” statements needs to be true to prove that a quadrilateral is a parallelogram
Example: Consecutive Angles of a Parallelogram are Supplementary
- If RAIL is a parallelogram, what is the value of x?
- Since consecutive angles are supplementary, 37 + 7x + 3 = 180
- Add constant terms: 40 + 7x = 180
- Subtract 40 from both sides: 7x = 140
- Divide both sides by 7: x = 20
Example: Opposite Sides of a Parallelogram are Congruent
- If UVWX is a parallelogram, what is the value of y?
- Since congruent sides are equal:
- Multiply by 3 on both sides: 39 = y