Claire thinks that if she draws a parallelogram with 2 congruent sides, it must be a rhombus. Jacob thinks that she would need to draw a parallelogram with at least 3 congruent sides before she could be sure it was a rhombus. Who is correct, if anyone, and why?
Claire is correct, because if the figure is a parallelogram and 2 sides are congruent, it must have all 4 sides congruent.
Jacob is correct, because a parallelogram with 4 congruent sides must have 2 pairs of opposite sides that are congruent.
Both are correct because if a figure has at least 2 congruent sides, it must have 4 congruent sides.
Neither is correct because one would need to draw 4 congruent sides in order to be sure the figure was a rhombus.
Answers
Answer:
A rhombus has all sides equal that is four congruent sides.
Statement of Claire
If she draws a parallelogram with 2 congruent sides, it must be a rhombus.
As Rhombus has four Congruent sides.2 Congruent sides does not Guarantee that the Parallelogram will be Rhombus.If Adjacent sides are congruent than Claire statement will be right otherwise not.
Statement of Jacob
If Jacob draws a parallelogram with at least 3 congruent sides ,it must be a rhombus.
Yes ,three congruent sides Guarantees that Parallelogram will be a rhombus because in a Parallelogram opposite sides are equal to each other.So congruency of three sides in a Parallelogram guarantees that this Parallelogram will be a rhombus.
So, we can Conclude that Jacob is correct.
Step-by-step explanation:
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A rhombus has all sides equal that is four congruent sides.
Statement of Claire
If she draws a parallelogram with 2 congruent sides, it must be a rhombus.
As Rhombus has four Congruent sides.2 Congruent sides does not Guarantee that the Parallelogram will be Rhombus.If Adjacent sides are congruent than Claire statement will be right otherwise not.
Statement of Jacob
If Jacob draws a parallelogram with at least 3 congruent sides ,it must be a rhombus.
Yes ,three congruent sides Guarantees that Parallelogram will be a rhombus because in a Parallelogram opposite sides are equal to each other.So congruency of three sides in a Parallelogram guarantees that this Parallelogram will be a rhombus.
So, we can Conclude that Jacob is correct.