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Which set of statements would describe a parallelogram that can always be classified as a rhombus? I. Diagonals are perpendicular bisectors of each other. II. Diagonals bisect the angles from which they are drawn. III. Diagonals form four congruent isosceles right triangles. 1. I and II 2. I and III 3. II and III 4. I, II, and III

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Answer:

1. I, II,

Step-by-step explanation:

I. Diagonals are perpendicular bisectors of each other  

Yes, because 4 sides are congruent so it makes the two diagonals perpendicular bisectors

II. Diagonals bisect the angles from which they are drawn

Yes, That is the property of the diagonal!

III. Diagonals form four congruent isosceles right triangles.

No, only two pairs of right triangles are congruent and sometime the side of each pair are different to each other.

Hence, we choose I and II

The statement I and II are the correct statements which describe a parallelogram that can always be classified as a rhombus.Thus option 1 is correct option.

Given-

  • Parallelogram-Parallelogram has 4 sides and it is a convex polygon.Its opposite sides are parallel and equal. Its opposite angle are also equal. The diagonals of the parallelogram bisects each other.

  • Rhombus-Rhombus is a type of parallelogram in which all sides are of equal length. In a rhombus the opposite sides are parallel. The diagonals of the rhombus bisects each other at 90 degrees. The most impotent thing of a rhombus is every rhombus is a parallelogram.

So a parallelogram which is a rhombus as well should follow the statements,

  • Diagonals are perpendicular bisectors of each other- As in a parallelogram which is rhombus all sides must be congruent. For this diagonal must be perpendicular bisectors of each other. Hence the statement I is correct.

  • Diagonals bisect the angles from which they are drawn-According to the properties of the diagonal, A diagonals bisects the angles from which they are drawn. Hence the statement II is correct.

  • Diagonals form four congruent isosceles right triangles-As in the rhombus the two congruent isosceles right triangles are formed. Hence this is incorrect statement.

Hence, The statement I and II are the correct statements which describe a parallelogram that can always be classified as a rhombus.Thus option 1 is correct option.

For more about the parallelogram, follow the  link below,

https://brainly.com/question/1563728

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