Properties Of Parallelograms! Geometry Trivia Quiz

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Quizzes Created: 29 | Total Attempts: 20,659

Questions: 5 | Attempts: 237 | Updated: Mar 19, 2023

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Properties Of Parallelograms! Geometry Trivia Quiz - Quiz

Questions and Answers

1.

In parallelogram ABCD, angle B = 3x + 20 degrees and angle D = 4x - 10 degrees. Find x.

Explanation
In a parallelogram, opposite angles are equal. Therefore, angle B is equal to angle D. By equating the given expressions for angle B and angle D, we can solve for x. 3x + 20 = 4x - 10. Simplifying the equation, we get x = 30. Therefore, the value of x is 30, and both angle B and angle D are equal to 30 degrees.

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2.

In parallelogram ABCD, AB = 3x + 4 and CD = 12x - 5. Find the length of CD.

Explanation
The length of CD can be found by setting the expressions for AB and CD equal to each other and solving for x. By doing this, we can determine that x = 3. Substituting this value back into the expression for CD, we find that CD = 12(3) - 5 = 36 - 5 = 31. Therefore, the length of CD is 31.

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3.

In parallelogram ABCD, angle A = 2x + 20 degrees and angle B = 4x + 10 degrees. Find the measure of angle A.

Explanation
The measure of angle A in parallelogram ABCD can be found by setting the given equation equal to the measure of angle A and solving for x. Once x is found, it can be substituted back into the equation to find the measure of angle A. In this case, setting 2x + 20 equal to 70 and solving for x gives x = 25. Substituting x = 25 back into the equation gives 2(25) + 20 = 70, confirming that the measure of angle A is indeed 70 degrees.

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4.

In parallelogram ABCD, diagonal AC = 16 and AE = 4x. Find x.

Explanation
In a parallelogram, the diagonals bisect each other. Therefore, AE is equal to EC. Given that AC is 16, AE is half of that, which is 8. Since AE is also equal to 4x, we can set up the equation 4x = 8 and solve for x. Dividing both sides by 4, we find that x = 2.

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5.

In parallelogram ABCD, BE = 5x - 2 and DE = 3x + 8. Find the length of BD.

Explanation
The length of BD can be found by adding the lengths of BE and DE, since BD is the diagonal of the parallelogram. Therefore, BD = BE + DE = (5x - 2) + (3x + 8) = 8x + 6. Since the value of x is not given, we cannot determine the exact length of BD. Therefore, the answer cannot be 46.

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