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. Find the length of diagonal of the trapezoid. Refer to the above diagram, which shows Trapezoid with diagonal. To the nearest whole number, give the length of.
To illustrate how to determine the correct length, draw a perpendicular segment from to , calling the point of intersection. Opposite sides of a rectangle are congruent, so. The two angles of a trapezoid along the same leg - in particular, and - are supplementary, so. Opposite sides of a rectangle are congruent, so , and. Set and :.
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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:. Report an Error. Find the length of both diagonals of this quadrilateral. 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.
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 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.
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. We now take the square root of both sides:. Explanation : 1 The diagonal can be found from by using the Pythagorean Theorem. Figure NOT drawn to scale. Explanation : To illustrate how to determine the correct length, draw a perpendicular segment from to , calling the point of intersection.
The two angles of a trapezoid along the same leg - in particular, and - are supplementary, so By the 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 :. The two angles of a trapezoid along the same leg - in particular, and - are supplementary, so By the Triangle Theorem, and is the hypotenuse of right triangle , so by the Pythagorean Theorem, its length can be calculated to be Set and :.
Copyright Notice. Together we are going to put our knowledge to the test, and discover some amazing properties about these three special parallelograms. First, it is important to note that rectangles, squares, and rhombi plural for rhombus are all quadrilaterals that have all the properties of parallelograms. The biggest distinguishing characteristics deal with their four sides and four angles.
A rectangle is a parallelogram with four right angles. A rhombus , which is sometimes called a rhomb or diamond, as Math is Fun nicely states, is a parallelogram with four congruent sides.
And a square is a parallelogram with four right angles and four congruent sides. Q: What is the difference between a rhombus and a parallelogram?
A: For a rhombus we are quaranteed that all the sides have the same length, while a parallelogram only specifies that opposite sides are congruent. Q: What is the difference between a square and a rhombus?
A: A square and a rhombus both have four congruent sides, but a square also has four congruent right angles, whereas a rhombus only specifies that opposite angles are congruent and they do not need to be 90 degrees. Q: Why is a square a rectangle? A: A square is a rectangle because it fulfills all the properties of a rectangle.
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