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Lesson 5 of 15

What a parallelogram gives you

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A charpai frame leans sideways when pushed. The four lengths of wood do not change. Why do the corners still change size?

Parallelogram ABCD: both pairs of sides parallel.
Step 1 of 4
  1. Parallelogram ABCD: both pairs of sides parallel.
  2. AD crosses parallel AB and DC: A + D = 180°.
  3. AB crosses parallel AD and BC: A + B = 180°.
  4. So B = D. The same steps give A = C.

Four fixed sides do not fix the corners. Next-door corners share a side. In a parallelogram, each next-door pair totals 180°. So when one grows, the other shrinks.

Rule: When both pairs of opposite sides are parallel, three facts follow. Match means equal.

  • Next-door angles total 180°.
  • Opposite angles match.
  • Opposite sides match — diagonal AC makes two triangles that match exactly.

Going round, a parallelogram's corners are 65°, 115°, 65° and 115°. Next-door corners: 65 + 115 = 180. Opposite corners: 65 = 65 and 115 = 115.

Watch out!

These facts need both pairs of sides parallel. Corners 100°, 80°, 90°, 90° total 360°, but no opposite pair matches. So that shape is not a parallelogram.

Drag the slider to change corner A. Watch the other corners.

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