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!
Isosceles trapezoid and rectangle
No but the diagonals are equal in length
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.
Its diagonals are equal in length
no but the trapezoid has 2 sets of parallellines
Quite simply providing that it is an isosceles trapezoid otherwise you'll need to know the lengths of the 2 diagonals
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.
It is an isosceles trapezoid.
A rectangle, a square, and an isosceles trapezoid.
Rectangle and Isosceles Trapezoid
No but the diagonals are equal in length
Isosceles trapezoid and rectangle
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.
trapezoid
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.
The diagonals of a square. Each equals to s√2, where s is the side-length of the square. A rectangle and an isosceles trapezoid also have congruent diagonals.
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.