Proving a Quadrilateral Is a Parallelogram

Question 1

are being used to get the equation in step 6.

Revolt · Accepted Answer

Steps 4 and 5; are being used to get the equation in step 6.: Steps 4 and 5; are being used to get the equation in step 8.: Steps 5 and 7; are being used to get the equation in step 9.: Steps 8 and 6; In step 14, "similar argument" means to draw segment and follow the same logic in steps 3-12.: BD

Question 2

are being used to get the equation in step 8.

Revolt · Accepted Answer

Steps 5 and 7

Question 3

are being used to get the equation in step 9.

Revolt · Accepted Answer

Steps 8 and 6

Question 4

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

Revolt · Accepted Answer

BD

Question 5

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

AED; 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 par: AED; 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 par: SAS; 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 par: ACB; 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 par: alternate interior angles

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

SAS

Question 7

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

ACB

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

alternate interior angles

Question 9

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

Revolt · Accepted Answer

9

Question 10

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

Revolt · Accepted Answer

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

Proving a Quadrilateral Is a Parallelogram Answers

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