-2, -2

Question

3, 2
6, -1
2, -1.5
1, -5
Which of the following statements provides enough information to prove that ABCD
is a parallelogram?

(1 point)
Responses

Sides AB
and CD
are both approximately 6.4 units. Since one pair of opposite sides are congruent, this proves that ABCD
is a parallelogram.
Sides upper A upper B and upper C upper D are both approximately 6.4 units. Since one pair of opposite sides are congruent, this proves that upper A upper B upper C upper D is a parallelogram.

Sides AD
and BC
are both approximately 4.2 units. Sides AB
and CD
are both approximately 6.4 units. Since both pairs of opposite sides are congruent, this proves that ABCD
is a parallelogram.
Sides upper A upper D and upper B upper C are both approximately 4.2 units. Sides upper A upper B and upper C upper D are both approximately 6.4 units. Since both pairs of opposite sides are congruent, this proves that upper A upper B upper C upper D is a parallelogram.

Sides AD
and DE
are both approximately 3.2 units. Sides AB
and BC
are both approximately 5.0 units. Since two pairs of adjacent sides are congruent, this proves that ABCD
is a parallelogram.
Sides upper A upper D and upper B upper C are both approximately 3.2 units. Sides upper A upper B and upper C upper D are both approximately 5.0 units. Since two pairs of adjacent sides are congruent, this proves that upper A upper B upper C upper D is a parallelogram.

Segments AE
and CE
are both approximately 4.0 units. Since line AC
is bisected, this proves that ABCD
is a parallelogram.

Answer 1

To determine which statement provides enough information to prove that ABCD is a parallelogram, we need to recall the properties of parallelograms:

1. Opposite sides of a parallelogram are congruent.
2. The diagonals of a parallelogram bisect each other.

Based on this understanding, we can analyze the given statements:

1. Sides AB and CD are both approximately 6.4 units. Since one pair of opposite sides are congruent, this proves that ABCD is a parallelogram.

   • This statement is correct since having one pair of opposite sides congruent is sufficient to prove that ABCD is a parallelogram.

2. Sides AB and CD are both approximately 6.4 units. Since one pair of opposite sides are congruent, this proves that ABCD is a parallelogram.

   • This is the same as the first option and also correct.

3. Sides AD and BC are both approximately 4.2 units. Sides AB and CD are both approximately 6.4 units. Since both pairs of opposite sides are congruent, this proves that ABCD is a parallelogram.

   • This statement is correct as it establishes that both pairs of opposite sides are congruent.

4. Sides AD and BC are both approximately 4.2 units. Sides AB and CD are both approximately 6.4 units. Since both pairs of opposite sides are congruent, this proves that ABCD is a parallelogram.

   • This is the same as the previous option and is correct.

5. Sides AD and DE are both approximately 3.2 units. Sides AB and BC are both approximately 5.0 units. Since two pairs of adjacent sides are congruent, this proves that ABCD is a parallelogram.

   • This is not sufficient. Two pairs of adjacent sides being congruent does not necessarily imply that the figure is a parallelogram.

6. Sides AD and BC are both approximately 3.2 units. Sides AB and CD are both approximately 5.0 units. Since two pairs of adjacent sides are congruent, this proves that ABCD is a parallelogram.

   • This is also not sufficient for the same reason as the previous statement.

7. Segments AE and CE are both approximately 4.0 units. Since line AC is bisected, this proves that ABCD is a parallelogram.

   • This statement is also sufficient, as proving that one diagonal bisects the other confirms that ABCD is a parallelogram.

In conclusion, the statements that provide enough information to prove that ABCD is a parallelogram are:

• Sides AB and CD are both approximately 6.4 units. Since one pair of opposite sides are congruent, this proves that ABCD is a parallelogram.
• Sides AD and BC are both approximately 4.2 units. Sides AB and CD are both approximately 6.4 units. Since both pairs of opposite sides are congruent, this proves that ABCD is a parallelogram.
• Segments AE and CE are both approximately 4.0 units. Since line AC is bisected, this proves that ABCD is a parallelogram.

If you need to choose just one answer, pick either of the first three options.

Answer 2

which is the better option?

Answer 3

Among the options provided, the best choice is the one that confirms both pairs of opposite sides are congruent, as this is a stronger and more definitive proof of ABCD being a parallelogram. Therefore, the best option is:

Sides AD and BC are both approximately 4.2 units. Sides AB and CD are both approximately 6.4 units. Since both pairs of opposite sides are congruent, this proves that ABCD is a parallelogram.

This statement gives the most robust evidence for ABCD being a parallelogram, as it establishes that both pairs of opposite sides are equal, which is a key property of parallelograms.