A trapezoid, or trapezium, is a quadrilateral which has a pair of parallel sides. The two parallel sides are called the trapezoid's bases, and the two non-parallel sides are referred to as the legs.
For any trapezoid, the following two correspond:
(1) Like any other quadrilateral, the degree measures of the four angles add up to 360 degrees. Thus the trapezoid shown in the figure above satisfies the following:
(2) Two angles on the same side of a leg are always supplementary, that is, they add up to 180 degrees. Thus for the trapezoid shown above, we have
The area of a trapezoid is found using the formula , where and are length of the parallel sides and is the perpendicular height of the trapezoid.
An isosceles trapezoid is a trapezoid that has congruent legs.
Thus, for the isosceles trapezoid in the figure above, the following correspond:
(1) The bases are parallel.
(2) The legs are equal in length. Thus,
(3) The angles the two legs make with a base are equal. Thus, and
If in the trapezoid above, what is
Since a trapezoid is a quadrilateral, the sum of its four internal angles must equal Hence we have
The figure above depicts an isosceles trapezoid.
If the length of is 5, what is the length of
An isosceles trapezoid is a trapezoid that has congruent legs. Thus, the lengths of and are equal, i.e.
The above figure depicts a trapezoid where If then what is
Since two angles on the same side of a trapezoid's leg add up to
The above figure depicts an isosceles trapezoid. If then what is
In an isosceles trapezoid, the angles on either side of the bases are the same. Thus, it follows that
Since two angles on the same side of a trapezoid's leg are supplementary, we know that
The above figure shows an isosceles trapezoid where If and then what is
Let points and be the perpendicular foots on from points and respectively. Then we have
Since the problem states that is an isosceles trapezoid, we know that Given that the length of is twice the length of we have and since the length ratio of the hypotenuse and the base of is is
We know that is an isosceles triangle, so and since it follows that
From (1) and (2), we know that and Hence we have