Fix the mistake: Properties of Parallelograms

Parallelograms ① Definition and Properties

A quadrilateral whose two pairs of opposite sides are respectively parallel is called a parallelogram.

Properties of Parallelograms

  • Opposite sides are respectively equal (AB=DC, AD=BC)
  • Opposite angles are respectively equal (∠A=∠C, ∠B=∠D)
  • The diagonals intersect at their respective midpoints (AO=CO, BO=DO)
Example ①
In parallelogram ABCD, when AB=6, AD=4, and ∠A=70°, find DC, BC, and ∠C.
Answer: DC=AB=6, BC=AD=4, ∠C=∠A=70°
Key Points
  • Opposite sides are equal and parallel
  • Opposite angles are equal
  • The diagonals intersect at their midpoints (bisect each other)

Practice Problems

  1. In parallelogram ABCD, let O be the intersection of the diagonals. When AO=5, find AC.
  2. When ∠A=110°, find ∠B.

Answers and Explanations

  1. Answer: AC=10. Since AO=CO=5, AC=2×5=10.
  2. Answer: ∠B=70°. ∠A+∠B=180° (the sum of adjacent angles).

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