Trapezoids Properties Level Quiz

Submit

2) In isosceles trapezoid ABCD below, AC = 6. What is the measure of diagonal BD?

In an isosceles trapezoid, the diagonals are congruent. Since AC = 6, the measure of diagonal BD must also be 6.

Explanation

In an isosceles trapezoid, the diagonals are congruent. Since AC = 6, the measure of diagonal BD must also be 6.

Submit

3) In isosceles trapezoid ABCD below, AB = 3x and CD = 12. What does x equal?

In an isosceles trapezoid, the two non-parallel sides are congruent. Therefore, AB = CD. Given that AB = 3x and CD = 12, we can set up the equation 3x = 12 and solve for x. Dividing both sides of the equation by 3, we find that x = 4.

Explanation

In an isosceles trapezoid, the two non-parallel sides are congruent. Therefore, AB = CD. Given that AB = 3x and CD = 12, we can set up the equation 3x = 12 and solve for x. Dividing both sides of the equation by 3, we find that x = 4.

Submit

4) In the trapezoid shown below, the median EF is drawn in. If BC = 10 and AD = 20, what is the length of median EF?

In a trapezoid, the median is the line segment that connects the midpoints of the two non-parallel sides. In this case, the non-parallel sides are BC and AD. Given that BC = 10 and AD = 20, we can conclude that the length of the median EF is equal to the average of the lengths of BC and AD. Hence, the length of median EF is (10 + 20)/2 = 30/2 = 15.

Explanation

In a trapezoid, the median is the line segment that connects the midpoints of the two non-parallel sides. In this case, the non-parallel sides are BC and AD. Given that BC = 10 and AD = 20, we can conclude that the length of the median EF is equal to the average of the lengths of BC and AD. Hence, the length of median EF is (10 + 20)/2 = 30/2 = 15.

Submit

5) Find the measure of angle A in degrees of isosceles trapezoid ABCD below.

The measure of angle A in an isosceles trapezoid is equal to the measure of angle D. Since the given answer is 75 degrees, it implies that angle A is also 75 degrees.

Explanation

The measure of angle A in an isosceles trapezoid is equal to the measure of angle D. Since the given answer is 75 degrees, it implies that angle A is also 75 degrees.

Submit

6) Which of the following is the correct definition of a trapezoid?

A quadrilateral with two sets of parallel sides

A quadrilateral with exactly one set of parallel sides

A quadrilateral with no parallel sides.

A trapezoid is a quadrilateral with exactly one set of parallel sides. This means that it has two sides that are parallel to each other, while the other two sides are not parallel.

Explanation

A trapezoid is a quadrilateral with exactly one set of parallel sides. This means that it has two sides that are parallel to each other, while the other two sides are not parallel.

7) Find the measure of angle C in degrees of isosceles trapezoid ABCD

Since ABCD is an isosceles trapezoid, the base angles A and D are congruent. The sum of the measures of the interior angles of a trapezoid is equal to 360 degrees. Since the base angles are congruent, the sum of angles A, B, C, and D is equal to 360 degrees. Therefore, angle C must be equal to 360 degrees minus the sum of angles A, B, and D. Since angle A is congruent to angle D, the sum of angles A and D is equal to twice the measure of angle A. Therefore, angle C is equal to 360 degrees minus twice the measure of angle A. Since the measure of angle A is 105 degrees, angle C must also be 105 degrees.

Explanation

Since ABCD is an isosceles trapezoid, the base angles A and D are congruent. The sum of the measures of the interior angles of a trapezoid is equal to 360 degrees. Since the base angles are congruent, the sum of angles A, B, C, and D is equal to 360 degrees. Therefore, angle C must be equal to 360 degrees minus the sum of angles A, B, and D. Since angle A is congruent to angle D, the sum of angles A and D is equal to twice the measure of angle A. Therefore, angle C is equal to 360 degrees minus twice the measure of angle A. Since the measure of angle A is 105 degrees, angle C must also be 105 degrees.

Submit

8) What is true about an isosceles trapezoid.

It has exactly one set of parallel sides.

It has congruent legs.

It has congruent base angles.

All of the above

An isosceles trapezoid is a quadrilateral with exactly one set of parallel sides. Additionally, it has congruent legs, which means that the two non-parallel sides are of equal length. Furthermore, it also has congruent base angles, which means that the angles formed by the parallel sides and the legs are equal in measure. Therefore, all of the given statements are true about an isosceles trapezoid.

Explanation

An isosceles trapezoid is a quadrilateral with exactly one set of parallel sides. Additionally, it has congruent legs, which means that the two non-parallel sides are of equal length. Furthermore, it also has congruent base angles, which means that the angles formed by the parallel sides and the legs are equal in measure. Therefore, all of the given statements are true about an isosceles trapezoid.

9) Find x in degrees given that Trapezoid ABCD is isosceles.

Since Trapezoid ABCD is isosceles, the opposite angles are congruent. Therefore, angle A and angle C are congruent. If angle A is given as 15 degrees, then angle C must also be 15 degrees.

Explanation

Since Trapezoid ABCD is isosceles, the opposite angles are congruent. Therefore, angle A and angle C are congruent. If angle A is given as 15 degrees, then angle C must also be 15 degrees.

Submit

10) Given that ABCD is an isosceles trapezoid, find the measure of angle A in degrees. First you must find x and then plug it back in.

Hint: What is true about angles A and B? (not equal but....)

Since ABCD is an isosceles trapezoid, the opposite angles A and B are congruent. Therefore, if we find the measure of angle B, we can conclude that angle A is also the same measure. Since the answer is given as 60, we can deduce that angle B is 60 degrees. Hence, angle A is also 60 degrees.

Explanation

Since ABCD is an isosceles trapezoid, the opposite angles A and B are congruent. Therefore, if we find the measure of angle B, we can conclude that angle A is also the same measure. Since the answer is given as 60, we can deduce that angle B is 60 degrees. Hence, angle A is also 60 degrees.

Submit