Common Core: High School - Geometry : Prove Parallelogram Theorems: CCSS.Math.Content.HSG-CO.C.11
Study concepts, example questions & explanations for Common Core: High School - Geometry
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Example Questions
Example Question #1 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
What is known if 
Opposite side lengths are parallel.
All of the other answers are correct.
All of the other answers are correct.
A parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel.
Drawing the parallelogram 
Looking at the image it can be said that,
Therefore, all of the possible answer choices are correct.
Example Question #1 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Which of the following helps prove an image is a parallelogram?
One Set of Parallel Lines
Two Lines must be Perpendicular
Congruent Opposite Angles
None of the other answers.
Angles that Exceed
Congruent Opposite Angles
A parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Example Question #2 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Which of the following helps prove an image is a parallelogram?
Two Lines must be Perpendicular
None of the other answers
One Set of Parallel Lines
Bisecting Diagonals
Angles that Exceed
Bisecting Diagonals
A parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Example Question #3 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Which of the following helps prove an image is a parallelogram?
Two Lines must be Perpendicular
Two Sets of Opposite Parallel Lines
Angles that Exceed
One Set of Parallel Lines
All of the answers are correct
Two Sets of Opposite Parallel Lines
A parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Example Question #5 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false:
A rhombus is an example of a parallelogram.
True
False
True
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. Since a rhombus has all of these characteristics it too is considered a parallelogram.
Therefore, the statement is true.
Example Question #6 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false:
A trapezoid is a parallelogram.
False
True
False
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
A trapezoid has one set of opposite parallel sides however, they are not congruent. The opposite angles of a trapezoid are also not congruent therefore, the statement is false.
Example Question #4 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false:
A quadrilateral 
False
True
False
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Since the statement only says that 
Example Question #5 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false:
In the figure 
False
True
True
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Since the angles given represent those in a parallelogram, and the opposite sides are congruent, that makes the figure a parallelogram.
Therefore, the statement is true.
Example Question #8 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false.
Bisecting a parallelogram along one of its diagonals creates two congruent triangles.
False
True
True
Given the statement:
"Bisecting a parallelogram along one of its diagonal creates two congruent triangles."
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. When a parallelogram is bisected along one of its diagonals it in fact creates two congruent triangles.
Therefore, the statement is true.
Example Question #9 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false:
To determine whether a figure is a parallelogram, you only need information on one pair of sides or one pair of angles.
False
True
False
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Since the statement gives one pair of sides and one pair of angles but does not specify whether the pairs are opposite it cannot be determined whether the figure is a parallelogram or not.
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