The diagonals of an isosceles trapezoid are represented by 2x - 7 and x + 1 what is the value of x

19 Questions | Total Attempts: 5689

• How do you describe any two opposite angles in a parallelogram?

  • They are always congruent.

  • They are both right angles.

• What can you say about any two consecutive angles in a parallelogram?

  • They are always congruent.

  • They are always supplementary.

  • They are sometimes complementary.

  • They are both right angles.

• Which of the following statements is true?

  • Every square is a rectangle.

  • Every rectangle is a square.

  • Every rhombus is a rectangle.

  • Every parallelogram is a rhombus.

• Which of the following statements could be false?

  • The diagonals of a rectangle are congruent.

  • The diagonals of an isosceles trapezoid are congruent.

  • The diagonals of a square are perpendicular and bisect each other.

  • The diagonals of a rhombus are congruent but not perpendicular to each other.

• Which of the following quadrilaterals has diagonals that do not bisect each other?

• Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram?

  • Two pairs of sides are parallel.

  • Two pairs of opposite sides are congruent.

  • Two angles are complementary.

  • Two diagonals bisect each other.

• What is the measurement of < 2 in rhombus HOME?

• Two consecutive angles of a parallelogram have measures (x + 30)° and [2(x – 30)]°. What is the measure of the smaller angle?

• Which of the following statements is true?

  • A trapezoid can have four equal sides.

  • A trapezoid can have three right angles.

  • The base angles of an isosceles trapezoid forms 90 degrees.

  • The diagonals of an isosceles trapezoid bisect each other.

• The diagonals of an isosceles trapezoid are represented by 4x – 47 and 2x + 31. What is the value of x? 

• A cross section of a water trough is in the shape of a trapezoid with bases measuring 2 m and 6 m. What is the length of the median of the trapezoid? 

• What are the measures of the sides of parallelogram SOFT in meters?

• Find the length of the longer diagonal in parallelogram FAST.

• Find the value of y in the figure below.

• In the rhombus RHOM, what is the measure of <ROH?

• In the rectangle KAYE, YO = 18 cm. Find the length of diagonal AE.

• What condition will make parallelogram WXYZ a rectangle?

  • Segment WX and segment YZ bisect each other.

• The perimeter of a parallelogram is 34 cm. If a diagonal is 1 cm less than its length and 8 cm more than its width, what are the dimensions of this parallelogram?

• Which of the following statements is/are true about isosceles trapezoid?

  • The diagonals are congruent.

  • The median is parallel to the bases.

• 9th Grade Biology
• 9th Grade Chemistry

What is the length of the diagonals of trapezoid 

? Assume the figure is an isoceles trapezoid.

Possible Answers:

Correct answer:

Explanation:

To find the length of the diagonal, we need to use the Pythagorean Theorem. Therefore, we need to sketch the following triangle within trapezoid 

:

We know that the base of the triangle has length

. By subtracting the top of the trapezoid from the bottom of the trapezoid, we get:

Dividing by two, we have the length of each additional side on the bottom of the trapezoid:

Adding these two values together, we get

.

The formula for the length of diagonal 

 uses the Pythagoreon Theorem:

, where  is the point between  and  representing the base of the triangle.

Plugging in our values, we get:

Find the length of both diagonals of this quadrilateral.

Possible Answers:

Correct answer:

Explanation:

All of the lengths with one mark have length 5, and all of the side lengths with two marks have length 4. With this knowledge, we can add side lengths together to find that one diagonal is the hypotenuse to this right triangle:

Using Pythagorean Theorem gives:

take the square root of each side

Similarly, the other diagonal can be found with this right triangle:

Once again using Pythagorean Theorem gives an answer of

Find the length of the diagonals of this isosceles trapezoid, with

.

Possible Answers:

Correct answer:

Explanation:

To find the length of the diagonals, split the top side into 3 sections as shown below:

The two congruent sections plus 8 adds to 14.

, so the two congruent sections add to 6. They must each be 3. This means that the top of the right triangle with the diagonal as a hypotenuse must be 11, since .

We can solve for the diagonal, now pictured, using Pythagorean Theorem:

take the square root of both sides

Find the length of the diagonal of the isosceles trapezoid given below. 

Possible Answers:

Correct answer:

Explanation:

In order to calculate the length of the diagonal, we first must assume that the height is perpendicular to both the top and bottom of the trapezoid. 

Knowing this, we can draw in the diagonal as shown below and use the Pythagorean Theorem to solve for the diagonal. 

We now take the square root of both sides: 

Find the length of diagonal

 of the trapezoid.

Possible Answers:

Correct answer:

Explanation:

1) The diagonal 

 can be found from  by using the Pythagorean Theorem.

2) The length of the base of 

,  has to be found because  is the length of the base of .

3)

.

4) Using the Pythagorean Theorem on

 to find ,

5) Using the Pythagorean Theorem on

 to find ,

Figure NOT drawn to scale.

Refer to the above diagram, which shows Trapezoid 

 with diagonal . To the nearest whole number, give the length of .

Possible Answers:

Correct answer:

Explanation:

To illustrate how to determine the correct length, draw a perpendicular segment from 

 to , calling the point of intersection .

 divides the trapezoid into Rectangle  and right triangle  .

Opposite sides of a rectangle are congruent, so 

.

. The two angles of a trapezoid along the same leg - in particular,  and  - are supplementary, so 

By the 30-60-90 Triangle Theorem,

Opposite sides of a rectangle are congruent, so 

, and

 is the hypotenuse of right triangle , so by the Pythagorean Theorem, its length can be calculated to be

Set

 and :

Figure NOT drawn to scale.

Refer to the above diagram, which shows Trapezoid 

 with diagonal . To the nearest whole number, give the length of .

Possible Answers:

Correct answer:

Explanation:

To illustrate how to determine the correct length, draw a perpendicular segment from  to , calling the point of intersection .

 divides the trapezoid into Rectangle  and right triangle  .

Opposite sides of a rectangle are congruent, so 

.

. The two angles of a trapezoid along the same leg - in particular,  and  - are supplementary, so 

By the 30-60-90 Triangle Theorem,

Opposite sides of a rectangle are congruent, so 

, and

 is the hypotenuse of right triangle 

, so by the Pythagorean Theorem, its length can be calculated to be

Set 

 and :

Figure NOT drawn to scale.

Refer to the above diagram, which shows Trapezoid

 with diagonal . To the nearest whole number, give the length of .

Possible Answers:

Correct answer:

Explanation:

To illustrate how to determine the correct length, draw a perpendicular segment from 

 to , calling the point of intersection .

 divides the trapezoid into Rectangle  and right triangle  .

Opposite sides of a rectangle are congruent, so 

.

. The two angles of a trapezoid along the same leg - in particular,  and  - are supplementary, so 

By the 45-45-45 Triangle Theorem,

and

 is the hypotenuse of right triangle 

, so by the Pythagorean Theorem, its length can be calculated to be

Set 

 and :

Rodrigo
Certified Tutor

University of California-Davis, Bachelor of Science, Applied Mathematics.

Isaias
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Instituto Tecnológico de Merida (ITM), Bachelor of Science, Biochemical Engineering. Yucatan Center for Scientific Research (...

Yatrik
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Government Engineering College, India, Bachelor of Engineering, Electrical Engineering. M.G. Science Institute, India, Bachel...

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