Common Core: High School - Geometry : Parallelogram Proofs
Study concepts, example questions & explanations for Common Core: High School - Geometry
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Example Questions
Example Question #13 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Which of the following is the definition of a parallelogram?
A quadrilateral with two pairs of opposite parallel sides
A quadrilateral with one pair of parallel sides
A quadrilateral with four right angles
A quadrilateral with four congruent sides and four congruent angles
A quadrilateral with two pairs of opposite parallel sides
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
Which of the following is the definition of a parallelogram?
A quadrilateral with one pair of parallel sides
A quadrilateral with two pairs of opposite parallel sides
A quadrilateral with four congruent sides and four congruent angles
A quadrilateral with four right angles
A quadrilateral with two pairs of opposite parallel sides
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
Which of the following is the definition of a parallelogram?
A quadrilateral with two pairs of opposite parallel sides
A quadrilateral with four right angles
A quadrilateral with one pair of parallel sides
A quadrilateral with four congruent sides and four congruent angles
A quadrilateral with two pairs of opposite parallel sides
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 #141 : Congruence
Prove that the following parallelogram has diagonals that prove two congruent triangles.
Proof:
Proof:
Proof:
Proof:
Example Question #141 : Congruence
Prove that the following parallelogram has four pairs of consecutive supplementary angles.
Proof:
Proof:
Proof:
Proof:
Thus, we have shown that this parallelogram has four pairs of consecutive supplementary angles.
Example Question #3 : Parallelogram Proofs
Prove the following parallelogram has two pairs of opposite congruent angles.
Proof:
Proof:
Proof:
Proof:
Example Question #7 : Parallelogram Proofs
Prove the following parallelogram has opposite congruent sides.
Proof:
Proof:
Proof:
Proof:
Thus, we have proven this parallelogram has congruent opposite sides.
Example Question #1 : Parallelogram Proofs
Prove that since this quadrilateral has two pairs of opposite congruent sides, it is a parallelogram.
Proof:
Proof:
Proof:
Proof:
Thus, we have shown that if a quadrilateral has two pairs of congruent opposite sides, then it is a parallelogram.
Example Question #9 : Parallelogram Proofs
True or False: Is the following quadrilateral a parallelogram?
False
True
True
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 #501 : High School: Geometry
Prove that if the following quadrilateral has a pair of opposite parallel, congruent sides, it is a parallelogram.
Proof:
Proof:
Proof:
Proof:
Thus, we have shown that if a quadrilateral has one pair of parallel, congruent opposite sides, then it is a parallelogram.
All Common Core: High School - Geometry Resources
