Question

1. error analysis ahmed uses the following explanation to prove that a figure is a parallelogram. what is ahmed’s error? the quadrilateral has a pair of opposite sides congruent and a pair of opposite sides parallel. according to theorem 6 - 15, the figure is a parallelogram.

Explanation:

The theorem (Theorem 6-15) requires that the same pair of opposite sides is both congruent and parallel. Ahmed's figure shows the congruent sides and parallel sides are different pairs of opposite sides, which does not satisfy the theorem. A quadrilateral with one pair of opposite sides parallel and a different pair congruent can be an isosceles trapezoid, not necessarily a parallelogram.

Answer:

Ahmed's error is that he applied the theorem to different pairs of opposite sides: the congruent sides and parallel sides are not the same pair. The theorem requires that a single pair of opposite sides is both congruent and parallel to prove a figure is a parallelogram.