Answered

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The measures of the three interior angles of a quadrilateral are 60°,60° and 120.Will this information be enough to conclude that the quadrilateral is a parallelogram? Explain your answer

Sagot :

Answer with explanation:

No, the given three measures of interior angles alone are not enough to conclude that a quadrilateral is a parallelogram.

To qualify that they are interior angles of a parallelogram:

  • Opposite angles of parallelogram are congruent.

  • In the given problem, the congruent angles at 60 degrees measure each must be specified as opposite angles. The given measures are not specified as such. If these congruent angles are consecutive or sharing the same side, then the quadrilateral is a trapezoid with its base angles measuring 120 degrees each.

The properties of parallelogram:

  • Opposite sides are parallel and congruent,
  • Opposite angles are congruent.
  • Its diagonal divides it into two congruent triangles.
  • The diagonals bisect each other.

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