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How would you construct a trapezoid given the length of the top and the bottom and the length of BOTH diagonals?
Consider the trapezium ABCD in which AD and BC are the top and the bottom - parallel and of known length - and AC and BD are the diagonals - also of known length. Suppose AC and BD intersect at O.
Then, it can be shown that triangles AOD and COB are similar. Therefore AO/OC = DO/OB = AD/BC where both lengths for the last ratio are known. Then, given AC, it is possible to calculate OC (and AO) and given BD, it is possible to calculate OB (and DO).
So all sides of triangle COB are known and so it is easy to construct it. Then simply extend BO to D (adding OD) and CO to A (adding OA). Join BA, AD and DC. Done!
What else can I help you with?
What quadrilaterals must have diagonals of equal length?
Isosceles trapezoid and rectangle
Can the parallel sides of an isosceles trapezoid be equal?
No but the diagonals are equal in length
Are diagonals of a trapezoid perpendicular?
Oh, dude, no way! Diagonals of a trapezoid are not necessarily perpendicular. It's like saying all cats are secretly plotting to take over the world - just because they're diagonal doesn't mean they're perpendicular, you know what I mean? So yeah, diagonals of a trapezoid can be any ol' angle they want, they don't have to be all right angles and stuff.
How would you construct an isosceles trapezoid given the length of the top and the bottom and the length of the diagonal?
A trapezoid is a quadrilateral with one pair of parallel sides. Within an isosceles trapezoid, the angles at the base will be identical, and the two sides will be congruent. If you have the length of the base and the top, and the length of the diagonal, you can build this figure. Draw a line for the base, as you already know its length. Then set your compass to the length of the diagonal. With that length set, place your compass on each end of the base you drew, and draw an arc starting along the line of the base and going up to a point straight up from the point of the compass, which is on the end of the base. The top of your isosceles trapezoid will have endpoints on these arcs and (naturally) be parallel to the base. With the base drawn and the two arcs scribed, find the difference between the length of the base and the length of the top of the trapezoid. With the difference calculated, divide this length in half, and measure in from the endpoints of your base and mark this point. The endpoints of the top of the trapezoid will be on a line that is the verticle from these points you marked. Make a right angle at the points, and then draw a line vertically to the arcs you scribed. Where the verticals intersect the arcs will be the endpoints of the top of the trapezoid. With those points now discovered, draw a line from one of them to the other, and that will be the top of your trapezoid. You have drawn your isosceles trapezoid from the dimensions of its base, top and its diagonal.
If a parallelogram is a rectangle then it's diagonals are what?
Its diagonals are equal in length
How would you construct a trapezoid given the length of the top and the bottom and the length of the diagonal?
Quite simply providing that it is an isosceles trapezoid otherwise you'll need to know the lengths of the 2 diagonals
Are the diagonals of a trapezoid always congruent?
No, the diagonals of a trapezoid are not always congruent. A trapezoid is a quadrilateral with at least one pair of parallel sides. The diagonals of a trapezoid connect the non-parallel vertices, and their lengths can vary depending on the specific dimensions of the trapezoid. In a trapezoid where the non-parallel sides are of equal length, the diagonals will be congruent, but this is not always the case.
Do the diagonals of a trapezoid bisect each other?
No, never. A trapezoid may have diagonals of equal length (isosceles trapezoid), but they do not intersect at their midpoints.Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. But this is a contradiction since the respective bases of the triangles, forming the top and bottom of the trapezoid are, of course, not equal. Therefore, the triangles cannot be congruent. Hence, we have given proof by contradiction that diagonals in a trapezoid cannot bisect each other.
What quadrilateral will have diagonals of equal length but will have no right angles?
It is an isosceles trapezoid.
Which quadrilaterals must have diagonals of equal length?
Rectangle and Isosceles Trapezoid
What quadrilateral have diagonals of equal length?
A rectangle, a square, and an isosceles trapezoid.
What quadrilaterals must have diagonals of equal length?
Isosceles trapezoid and rectangle
Can the parallel sides of an isosceles trapezoid be equal?
No but the diagonals are equal in length
What is an isosceles trapezoid?
It is a trapezoid in which the non-parallel sides are of the same length and subtend equal angles with the base. It can be viewed as an isosceles triangle whose apex has been removed by a line parallel to its base.
How would you construct an isosceles trapazoid if only given the base angles and the length of the diagonal?
You can't construct a specific trapezoid. You need to know the length of at least one other side, otherwise the width of the trapezoid is indeterminable.
A quadrilateral with equal diagonals and no right angles?
An isosceles trapezoid will have diagonals of equal length but will never contain right angles by definition. A square and rectangle will have diagonals of equal length but will contain 4 right angles. A rhombus and any other parallelogram that does not contain right angles will not have diagonals of equal length.
Are diagonals of a trapezoid perpendicular?
Oh, dude, no way! Diagonals of a trapezoid are not necessarily perpendicular. It's like saying all cats are secretly plotting to take over the world - just because they're diagonal doesn't mean they're perpendicular, you know what I mean? So yeah, diagonals of a trapezoid can be any ol' angle they want, they don't have to be all right angles and stuff.
