Common Core: High School - Geometry : Parallelogram Proofs

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Example Question #1 : Parallelogram Proofs

Which of the following is the definition of a parallelogram?

Possible Answers:

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with one pair of parallel sides

A quadrilateral with four right angles

Correct answer:

A quadrilateral with two pairs of opposite parallel sides

Explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.

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Opposite sides of a parallelogram are congruent as well as its opposite angles.

 

Example Question #1 : Parallelogram Proofs

Which of the following is the definition of a parallelogram?

Possible Answers:

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four right angles

Correct answer:

A quadrilateral with two pairs of opposite parallel sides

Explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.

Opposite sides of a parallelogram are congruent as well as its opposite angles.

 

Example Question #532 : High School: Geometry

Which of the following is the definition of a parallelogram?

Possible Answers:

A quadrilateral with four right angles

 

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

 

A quadrilateral with two pairs of opposite parallel sides

 

Correct answer:

A quadrilateral with two pairs of opposite parallel sides

 

Explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.

Opposite sides of a parallelogram are congruent as well as its opposite angles.

 

Example Question #1 : Parallelogram Proofs

Prove that the following parallelogram has diagonals that prove two congruent triangles.

Screen shot 2020 08 20 at 8.20.48 am

Possible Answers:

Proof:

Screen shot 2020 08 20 at 8.25.20 am

Proof:

Screen shot 2020 08 20 at 8.23.53 am

Proof:

Screen shot 2020 08 20 at 8.24.35 am

Correct answer:

Proof:

Screen shot 2020 08 20 at 8.23.53 am

Explanation:

Screen shot 2020 08 20 at 8.21.35 am

Example Question #4 : Parallelogram Proofs

Prove that the following parallelogram has four pairs of consecutive supplementary angles.

Screen shot 2020 08 07 at 2.42.05 pm

Possible Answers:

Proof:

Screen shot 2020 07 02 at 8.43.08 am

Proof:

Screen shot 2020 07 02 at 8.41.54 am

Proof:

Screen shot 2020 07 02 at 8.40.23 am

Correct answer:

Proof:

Screen shot 2020 07 02 at 8.40.23 am

Explanation:

Screen shot 2020 07 02 at 9.00.54 am

Thus, we have shown that this parallelogram has four pairs of consecutive supplementary angles.

Example Question #11 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

Prove the following parallelogram has two pairs of opposite congruent angles.

Screen shot 2020 08 12 at 9.45.17 am

Possible Answers:

Proof:

Screen shot 2020 07 02 at 11.29.51 am

Proof:

Screen shot 2020 07 02 at 11.34.57 am

Proof:

Screen shot 2020 07 02 at 11.25.50 am

Correct answer:

Proof:

Screen shot 2020 07 02 at 11.34.57 am

Explanation:

Screen shot 2020 07 02 at 11.45.31 am

Screen shot 2020 07 02 at 11.45.47 am

Example Question #491 : High School: Geometry

Prove the following parallelogram has opposite congruent sides.

Screen shot 2020 08 13 at 8.25.37 am

Possible Answers:

Proof:

Screen shot 2020 08 13 at 8.28.32 am

Proof:

Screen shot 2020 08 13 at 8.27.12 am

Proof:

Screen shot 2020 08 13 at 8.27.52 am

Correct answer:

Proof:

Screen shot 2020 08 13 at 8.27.12 am

Explanation:

Screen shot 2020 08 13 at 8.25.48 am

Thus, we have proven this parallelogram has congruent opposite sides.

Example Question #5 : Parallelogram Proofs

Prove that since this quadrilateral has two pairs of opposite congruent sides, it is a parallelogram.

Screen shot 2020 08 13 at 8.32.00 am

Possible Answers:

Proof:

Screen shot 2020 08 13 at 8.34.30 am

Proof:

Screen shot 2020 08 13 at 8.33.56 am

Proof:

Screen shot 2020 08 13 at 8.33.21 am

Correct answer:

Proof:

Screen shot 2020 08 13 at 8.34.30 am

Explanation:

Screen shot 2020 08 13 at 8.32.11 am

Thus, we have shown that if a quadrilateral has two pairs of congruent opposite sides, then it is a parallelogram.

Example Question #2 : Parallelogram Proofs

True or False: Is the following quadrilateral a parallelogram?

Screen shot 2020 08 20 at 8.35.53 am

Possible Answers:

True

False

Correct answer:

True

Explanation:

This is true because a theorem states that if a quadrilateral has two consecutive angles that are supplementary, then the quadrilateral is a parallelogram.

Example Question #2 : Parallelogram Proofs

Prove that if the following quadrilateral has a pair of opposite parallel, congruent sides, it is a parallelogram.

Screen shot 2020 08 20 at 9.22.22 am

Possible Answers:

Proof:

Screen shot 2020 08 20 at 9.23.33 am

Proof:

Screen shot 2020 08 20 at 9.24.06 am

Proof:

Screen shot 2020 08 20 at 9.24.46 am

Correct answer:

Proof:

Screen shot 2020 08 20 at 9.24.46 am

Explanation:

Thus, we have shown that if a quadrilateral has one pair of parallel, congruent opposite sides, then it is a parallelogram.

Screen shot 2020 08 20 at 9.22.33 am

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