Q: How many sides of a trapezoid have to be congruent to make it an isosceles trapezoid?

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A quadrilateral that has one (and only one) pair of parallel sides is a trapezoid. It is isosceles of the non-parallel sides are of equal length. It is right angled if any one of the angles is 90 degrees.

The fewest number of triangles that make up a trapezoid are two isosceles triangles.

Isosceles right angled triangle, as the remaining angle must be 90o.

Two Isosceles triangles.__ ^/ / / |/ / / |V --

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.

Related questions

The two outer sides

A quadrilateral that has one (and only one) pair of parallel sides is a trapezoid. It is isosceles of the non-parallel sides are of equal length. It is right angled if any one of the angles is 90 degrees.

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.

Yes. Any cut parallel to the base will do.

The fewest number of triangles that make up a trapezoid are two isosceles triangles.

A trapezoid is a quadrilateral shape that has four sides.

Isosceles right angled triangle, as the remaining angle must be 90o.

A quadrilateral that is not a parallelogram (two sets of parallel sides) may be a trapezoid or a trapezium (US terms). To draw a trapezium (irregular quadrilateral), draw two parallel lines and connect them with unequal lines at non-congruent angles. If you make the angles opposite and congruent, you have drawn a trapezoid, which looks like a small stepstool with a top smaller than the base. If you make the connecting lines of equal length, you have drawn a trapezoid or parallelogram.

Two Isosceles triangles.__ ^/ / / |/ / / |V --

make it have six sides

Isosceles triangle

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.