Proving a Quadrilateral Is a Parallelogram

Question 1

are being used to get the equation in step 6.

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C: Steps 4 and 5

Question 2

Determine the value of x that would make quadrilateral LMNO a parallelogram.

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B: 9

Question 3

By a similar argument used to prove that △AEB ≅ △CED, we can show that △ ≅ △CEB by. So, ∠CAD ≅ ∠ by CPCTC. Therefore, AD || BC by the converse of the theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Revolt · Accepted Answer

B: AED

Question 4

Based on the information given, is the quadrilateral a parallelogram? Explain.

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D: The figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent.

Question 5

are being used to get the equation in step 8.

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B: Steps 5 and 7

Question 6

By a similar argument used to prove that △AEB ≅ △CED, we can show that △ ≅ △CEB by. So, ∠CAD ≅ ∠ by CPCTC. Therefore, AD || BC by the converse of the theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Revolt · Accepted Answer

C: SAS

Question 7

are being used to get the equation in step 9.

Revolt · Accepted Answer

B: Steps 8 and 6

Question 8

By a similar argument used to prove that △AEB ≅ △CED, we can show that △ ≅ △CEB by. So, ∠CAD ≅ ∠ by CPCTC. Therefore, AD || BC by the converse of the theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Revolt · Accepted Answer

A: ACB

Question 9

In step 14, "similar argument" means to draw segment and follow the same logic in steps 3-12.

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C: BD

Question 10

By a similar argument used to prove that △AEB ≅ △CED, we can show that △ ≅ △CEB by. So, ∠CAD ≅ ∠ by CPCTC. Therefore, AD || BC by the converse of the theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Revolt · Accepted Answer

A: alternate interior angles

Proving a Quadrilateral Is a Parallelogram Answers

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