Question

true or false? every parallelogram is a rhombus. true false every rectangle is a parallelogram. true false every rectangle with four congruent sides is a square. true false every quadrilateral is a rhombus. true false

Explanation:

Step1: Recall parallelogram and rhombus def.

A parallelogram has opposite - sides parallel, while a rhombus has all - sides equal. Not all parallelograms have all - sides equal, so "Every parallelogram is a rhombus" is false.

Step2: Recall rectangle and parallelogram def.

A rectangle has opposite sides parallel and equal and all angles 90 degrees. Since opposite sides are parallel, every rectangle is a parallelogram, so this is true.

Step3: Recall rectangle and square def.

A square has all sides congruent and all angles 90 degrees. A rectangle with four congruent sides meets the definition of a square, so this is true.

Step4: Recall quadrilateral and rhombus def.

A quadrilateral is a four - sided polygon, and a rhombus is a special quadrilateral with all sides equal. Not all quadrilaterals have all sides equal, so "Every quadrilateral is a rhombus" is false.

Answer:

1. False
2. True
3. True
4. False