Two quadrilaterals with the same side lengths are always congruent.

Posted By Admin @ September 03, 2022

Question:

Select all statements

A. Two squares with the same lengths are always congruentB. Two rectangles with the same side lengths are always congruent C. two rhombuses with the same side lengths are always congruent D. two parallelograms with the same side lengths are always congruent E. two quadrilaterals with the same side lengths are always congruent ​

Answer:

The statements that are correct in the given question are: options A, B and C.

Quadrilaterals are figures or shape bounded by four straight sides. Thus each quadrilateral has its sum of interior angles to be 360^{o}. Examples include; rectangle, square, trapezium, rhombus, kite, parallelogram.

Considering the properties of each quadrilateral given in the question, it can be inferred that;

  • squares of equal length of sides are congruent.
  • rectangles of equal length of sides are congruent.
  • rhombuses with equal side lengths are congruent.
  • parallelogram with the same side lengths may not be congruent. This is because the angles of the slanting sides may not be the same.
  • quadrilaterals with the same side length may not congruent. Example: rectangle and parallelogram of the same side length are not congruent.

Therefore, the appropriate statements that are correct are: options A, B and C.

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