Can the following quadrilateral be proven to be a parallelogram based on the given information?
No. It is not a parallelogram because the angles of the quadrilateral do not add up to
360 degrees360°.
B.
No. It is not a parallelogram because one pair of opposite sides is not congruent and the other pair of opposite sides is congruent.
C.
Yes. It is a parallelogram because one pair of opposite sides is congruent and the other pair of opposite sides is parallel.
D.
Yes.
It is a parallelogram because one pair of opposite sides is congruent and parallel.It is a parallelogram because one pair of opposite sides is congruent and parallel.
(its a parallelogram with no numbers or letters just two < and - on two of the sides.)
I guess you'll just have to analyze the figure, which we cannot see. The choices tell you what to look at.
I don't know how to attach an attachment.
Based on the given information, option C is the correct answer. It states that the quadrilateral is a parallelogram because one pair of opposite sides is congruent and the other pair of opposite sides is parallel. The fact that the angles of the quadrilateral do not add up to 360 degrees is not relevant to determining whether or not it is a parallelogram. Option B is incorrect because it states that one pair of opposite sides is not congruent, which contradicts the given information. Option D is incorrect because it repeats the information given without providing any additional insight.
To determine if the given quadrilateral is a parallelogram, we need to assess the properties of a parallelogram.
A parallelogram is a quadrilateral with the following properties:
1. Opposite sides are parallel.
2. Opposite sides are congruent.
3. Opposite angles are congruent.
4. Consecutive angles are supplementary (add up to 180 degrees).
Let's evaluate the given answer choices:
A. No. It is not a parallelogram because the angles of the quadrilateral do not add up to 360 degrees.
This answer choice is incorrect because the sum of the angles in a quadrilateral is always 360 degrees, regardless of whether it is a parallelogram.
B. No. It is not a parallelogram because one pair of opposite sides is not congruent and the other pair of opposite sides is congruent.
This answer choice is correct. A quadrilateral can only be a parallelogram if both pairs of opposite sides are congruent, so if one pair is not congruent, it cannot be a parallelogram.
C. Yes. It is a parallelogram because one pair of opposite sides is congruent and the other pair of opposite sides is parallel.
This answer choice is incorrect if we consider all the properties of a parallelogram. While having one pair of opposite sides congruent and the other pair parallel is a necessary condition for a parallelogram, it is not sufficient. We also need the opposite sides to be congruent.
D. Yes. It is a parallelogram because one pair of opposite sides is congruent and parallel.
This answer choice is correct. A quadrilateral is considered a parallelogram when it satisfies the properties of having both pairs of opposite sides congruent and parallel.
Given that the description of the quadrilateral includes one pair of opposite sides that are congruent and parallel, we can conclude that it is a parallelogram. Therefore, the correct answer is D.