Common Core: High School - Geometry : Prove Parallelogram Theorems: CCSS.Math.Content.HSG-CO.C.11
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Example Question #11 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
How can a parallelogram be constructed given an isosceles triangle?
Draw two additional sides that are the same length as the sides of the triangle. The diagonal of the parallelogram will be one of the side lengths of the triangle.
A triangle cannot be used to construct a parallelogram.
Draw a reflected isosceles triangle where the base is shared and becomes the diagonal of the parallelogram.
Draw two additional sides that are the same length as the base of the triangle. The diagonal of the parallelogram will be one of the side lengths of the triangle.
None of the answers will create a parallelogram.
Draw a reflected isosceles triangle where the base is shared and becomes the diagonal of the parallelogram.
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 an isosceles triangle has two side lengths that are equal, if it is reflected over the base a rhombus is created which is a type of parallelogram.
If the isosceles triangle is rotated so that one of the sides is the diagonal of the parallelogram then the opposite sides of the parallelogram are congruent thus making the figure a parallelogram.
If side lengths are added the resulting image will have three equal sides and one side that isn't therefore, the new figure is not a parallelogram.
Thus, looking at the given answer options, "Draw a reflected isosceles triangle where the base is shared and becomes the diagonal of the parallelogram." is the best choice.
Example Question #11 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Determine whether the statement is true or false:
In the figure 
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 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.
Therefore, the statement is true.
Example Question #1 : Parallelogram Proofs
Which of the following is the definition of a parallelogram?
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
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 #2 : Parallelogram Proofs
Which of the following is the definition of a parallelogram?
A quadrilateral with four congruent sides and four congruent angles
A quadrilateral with four right angles
A quadrilateral with one pair of parallel sides
A quadrilateral with two pairs of opposite parallel sides
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 #142 : 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 #13 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
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.
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