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QuestionMathematics
What are the five properties of a parallelogram?
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Step 1:I'll solve this problem by listing the five key properties of a parallelogram:
Step 2:: Opposite Sides are Parallel
- Mathematically, this means $$\overline{AB} \parallel \overline{CD}$$ and $$\overline{AD} \parallel \overline{BC}
- In a parallelogram, the opposite sides are always parallel to each other
Step 3:: Opposite Sides are Equal in Length
- Symbolically: $$|\overline{AB}| = |\overline{CD}$$ and $$|\overline{AD}| = |\overline{BC}
- The opposite sides of a parallelogram have equal lengths
Step 4:: Opposite Angles are Congruent
- Mathematically: $$\angle A = \angle C$$ and $$\angle B = \angle D
- The opposite angles in a parallelogram have equal measure
Step 5:: Consecutive Angles are Supplementary
- This means: $$\angle A + \angle B = 180°$$ and $$\angle B + \angle C = 180°
- Adjacent angles in a parallelogram sum to 180 degrees
Step 6:: Diagonals Bisect Each Other
- If diagonal $$\overline{AC}$$ intersects diagonal $$\overline{BD}$$, they divide each other exactly in half
- The diagonals of a parallelogram intersect at their midpoint
Final Answer
These are the five fundamental properties that define a parallelogram: parallel opposite sides, equal opposite sides, congruent opposite angles, supplementary consecutive angles, and diagonals that bisect each other.
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