Properties Of Parallelograms! Geometry Trivia Quiz

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

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.

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.

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.

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, diagonal AC = 16 and AE = 4x. Find x.

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.

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

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.

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

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.

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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