Proving That a Quadrilateral Is a Parallelogram Quiz Part 1
1.(equilateral)
2.(128.6°)
3.(21)
4.(720°)
5.(x=99°)
6.(96°)
7.(5)
8.(essay question)
9.(Yes, both pairs of opposite sides are congruent.)
10.(essay question)
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It seems like you have shared a list of responses to a quiz or test about proving that a quadrilateral is a parallelogram. However, the list you provided does not include any questions.
To help you understand how to prove that a quadrilateral is a parallelogram, let me explain the basic criteria:
1. Opposite sides of a parallelogram are parallel: To prove that a quadrilateral is a parallelogram, you need to show that the opposite sides are parallel. You can do this by calculating the slopes of the sides. If the slopes are equal, the sides are parallel.
2. Opposite sides of a parallelogram are congruent: In addition to being parallel, opposite sides of a parallelogram are also congruent in length. To prove this, you can use distance formulas or congruence theorems.
3. Opposite angles of a parallelogram are congruent: Another property of parallelograms is that opposite angles are congruent. To prove this, you can use angle measurements or angle congruence theorems.
4. Consecutive angles of a parallelogram are supplementary: Consecutive angles in a parallelogram add up to 180 degrees. This can be proven using angle measurements or angle sum theorems.
By using these criteria and appropriate mathematical techniques, you can prove that a given quadrilateral is a parallelogram.