Hardest Quadrilaterals Test! Geometry Trivia Quiz

In a rectangle, opposite sides are equal in length. Therefore, if BC is 8 units long, then AD must also be 8 units long in order to maintain the rectangular shape.

Since angle C is given as 65° and angle E is represented as 5X, we can set up an equation: 5X = 65. Solving for X, we divide both sides by 5 to get X = 13. Therefore, the value of X is 13°.

The measure of angle A in parallelogram ABCD is 50 degrees. This can be determined by using the property of opposite angles in a parallelogram. Since angle B is given as 130 degrees, angle A, which is opposite to angle B, will also be 130 degrees. However, the sum of the measures of angles in a parallelogram is always 360 degrees. Therefore, angle A can be found by subtracting the measure of angle B from 360 degrees, which gives us 360 - 130 = 230 degrees. However, since angle A is opposite to angle B, it will have the same measure as angle B, which is 130 degrees. Therefore, the measure of angle A is 130 degrees.

The given information states that DE is equal to 7. Therefore, if BD is equal to 14, it means that BD is twice the length of DE. This implies that BD is equal to 2 times 7, which equals 14. Hence, the answer is 14 and BD is indeed equal to 14.

In a parallelogram, opposite angles are equal. Therefore, if one angle is 6, then the opposite angle must also be 6.

Since angle E is equal to 13X, and angle C is equal to 65, we can set up the equation 13X = 65. By dividing both sides of the equation by 13, we find that X = 5. Therefore, the value of X is 5°.

In a parallelogram, opposite angles are congruent. Since the measure of angle 1 is not given directly, we can determine it by finding the measure of the opposite angle. The given answer of 126° is correct because it is the measure of the opposite angle to angle 1 in the parallelogram.

In a parallelogram, opposite sides are equal in length. So if AB is the same as CD, we can set them equal to each other and solve for x.

Given: AB = 8x - 2 CD = 6x + 8

Since AB is equal to CD: 8x - 2 = 6x + 8

Now, let's solve for x: 8x - 6x = 8 + 2 2x = 10 x = 5

Now that we have found the value of x, we can substitute it back into AB to find the length of AB:

AB = 8x - 2 AB = 8(5) - 2 AB = 40 - 2 AB = 38

Therefore, the length of AB in the parallelogram is 38 units.

The sum of the angles in a parallelogram is 360 degrees. Therefore, we can set up the equation: (3x + 20) + (4x - 10) = 360. Simplifying the equation gives us 7x + 10 = 360. Subtracting 10 from both sides gives us 7x = 350. Dividing both sides by 7 gives us x = 50. Therefore, the value of x is 50.

Since ABCD is a rectangle, opposite sides are equal in length. Therefore, AG = DG. We can set up an equation using this information:

2j + 21 = -j + 39

Solving this equation, we find j = 6.

Now, we can substitute the value of j back into either AG or DG to find its length. Using AG:

AG = 2(6) + 21 = 33

Since opposite sides of a rectangle are equal, BD is also equal to 33.

In a parallelogram, the diagonals bisect each other. Therefore, AC is equal to BD. Given that AC = 32, we can conclude that BD is also equal to 32. Since AE is a diagonal, it is equal to BD. So, AE = 32. It is also given that AE = 4x. By equating the two expressions for AE, we get 4x = 32. Dividing both sides by 4, we find that x = 8. Hence, the value of x is 8.

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The quadrilateral in the diagram is a parallelogram because it has two pairs of parallel sides. A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length. It can also be identified by its opposite angles being equal. In the given diagram, the sides AB and CD are parallel, as well as the sides BC and AD. Therefore, the correct name for the quadrilateral in the diagram is parallelogram.

The measure of angle A in parallelogram ABCD is 70 degrees. This is determined by setting the given equation equal to 70 and solving for x. By substituting x = 25 into the equation for angle A, we find that angle A = 2(25) + 20 = 70 degrees.

The length of BD in parallelogram ABCD is 52.

In a parallelogram, opposite angles are congruent. Since angle J is opposite to angle 87, they must have the same measure. Therefore, angle J is also 87 degrees.

Rectangles are quadrilaterals with four right angles. Therefore, statement II is true. Additionally, rectangles have opposite sides that are congruent, as opposite sides are parallel and congruent. This makes statement I true. Lastly, the diagonals of a rectangle are congruent, as they bisect each other and form right angles. Hence, statement III is also true. Therefore, the correct answer is I, II, and III.

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The measure of angle B in parallelogram ABCD is 110 degrees. This can be determined by setting the measure of angle A equal to the measure of angle B (since opposite angles in a parallelogram are congruent) and solving for x. By substituting x back into the equation for angle B, we can find that the measure of angle B is indeed 110 degrees.

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To find the measure of angle F, we need to solve the equation(4x - 20)° = 61°, as opposite angles in a parallelogram are equal.

Let’s solve this equation:

4x - 20 = 61

4x = 61 + 20

4x = 81

x = 81/4

x = 20.25

So, the value of x is 20.25. Now, let’s substitute x into the expression for angle F:

F = 4x - 20

F = 4(20.25) - 20

F = 81 - 20

F = 61°

Therefore, the measure of angle F is 61°.

In a parallelogram, opposite angles are congruent. Since angle J is opposite to the angle measuring 97 degrees, the measure of angle J is also 97 degrees.

A trapezoid (also known as a trapezium in some regions) is a type of quadrilateral that has only one pair of parallel sides. The two sides that are not parallel are called the legs of the trapezoid. This distinguishes it from other quadrilaterals like rectangles or squares, which have two pairs of parallel sides. Therefore, trapezoid correctly fills the blank.