Which of the following statements is true about a parallelogram?A) Opposite sides are equal, but opposite angles are not.B) Opposite angles are equal, but opposite sides are not.C) Both opposite sides and opposite angles are equal.D) All sides are equal.
Question
Which of the following statements is true about a parallelogram?A) Opposite sides are equal, but opposite angles are not.B) Opposite angles are equal, but opposite sides are not.C) Both opposite sides and opposite angles are equal.D) All sides are equal.
Solution
The correct answer is C) Both opposite sides and opposite angles are equal.
Here's why:
A parallelogram is a four-sided figure with both pairs of opposite sides parallel. This gives it some special properties:
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Opposite sides of a parallelogram are equal in length. This means that if you were to measure the length of one side, it would be the same as the length of the side directly across from it.
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Opposite angles of a parallelogram are equal. This means that if you were to measure one angle, it would be the same as the angle directly across from it.
So, both statements A and B are incorrect because they only state half of the properties of a parallelogram. Statement D is also incorrect because not all sides of a parallelogram are equal - that's a property of a square or a rhombus, not a parallelogram.
Therefore, the only true statement about a parallelogram is C) Both opposite sides and opposite angles are equal.
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In the coordinate plane, quadrilateral ๐๐๐ ๐ has coordinates ๐(-4,2), ๐(0,5), ๐ (7,4), and ๐(3,1). Which of the following statements is true about quadrilateral ๐๐๐ ๐?ResponsesBecause the slope of ๐๐ยฏ is equal to the slope of ๐๐ ยฏ and the slope of ๐๐ ยฏ is equal to the slope of ๐๐ยฏ, ๐๐ยฏโฅ๐๐ ยฏ and ๐๐ ยฏโฅ๐๐ยฏ. Therefore, quadrilateral ๐๐๐ ๐ is a parallelogram.Answer A: Because the slope of line segment P Q is equal to the slope of line segment S R and the slope of line segment Q R is equal to the slope of line segment P S , line segment P Q is parallel to line segment S R and line segment Q R is parallel to line segment P S . Therefore, quadrilateral P Q R S is a parallelogram.ABecause the slope of ๐๐ยฏ is the opposite of the slope of ๐๐ ยฏ and the slope of ๐๐ ยฏ is the opposite of the slope of ๐๐ยฏ, ๐๐ยฏโฅ๐๐ ยฏ and ๐๐ ยฏโฅ๐๐ยฏ. Therefore, quadrilateral ๐๐๐ ๐ is a parallelogram.Answer B: Because the slope of line segment P Q is the opposite of the slope of line segment S R and the slope of line segment Q R is the opposite of the slope of line segment P S , line segment P Q is parallel to line segment S R and line segment Q R is parallel to line segment P S . Therefore, quadrilateral P Q R S is a parallelogram.BBecause the slope of ๐๐ ยฏ is not the opposite of the slope of ๐๐ยฏ, ๐๐ ยฏ is not perpendicular to ๐๐ยฏ. Therefore, quadrilateral ๐๐๐ ๐ is not a parallelogram.Answer C: Because the slope of line segment P R is not the opposite of the slope of line segment Q S , line segment P R is not perpendicular to line segment Q S . Therefore, quadrilateral P Q R S is not a parallelogram.CBecause the slope of ๐๐ ยฏ is not the opposite reciprocal of the slope of ๐๐ยฏ, ๐๐ ยฏ is not perpendicular to ๐๐ยฏ. Therefore, quadrilateral ๐๐๐ ๐ is not a parallelogram.
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