The mid-line of a trapezoid is parallel to its bases. Since |BG| = |DC| from the triangles congruency, we have |EF| = 1/2*(|AB| + |DC|), or |EF| = 1/2*(a + d), where a and d are the lengths of the trapezoid bases. In our case, the length of the segment EF is half of the length AG : |EF| = 1/2*|AG| = 1/2*(|AB| + |BG|). The base angles of an isosceles trapezoid are congruent. An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent. A trapezoid is a quadrilateral with exactly one pair of parallel sides. It is well known fact that the the straight line segment connecting the midpoints of the triangle AGD is parallel to the triangle base AG and its length is half of the length of the triangle base. Determine unknown angle measurements of quadrilaterals with exactly one pair of parallel sides. Thus the mid-line EF of the trapezoid ABCD is the straight line segment connecting the midpoints of the triangle AGD. It implies that the segments DF and GF are congruent as the corresponding sides of the congruent triangles DFC and FBG. Hence, the triangles DFC and FBG are congruent in accordance with the ASA-test of congruency of triangles. The angles DCF and FBG are congruent as the alternate exterior anglesĪt the parallel lines AB and DC and the transverse BC. The angles DFC and BFG are congruent as the vertical angles. Well we could see these two non-parallel sides do not have the same. Now an isosceles trapezoid is a trapezoid where the two non-parallel sides have the same length, just like an isosceles triangle, you have two sides have the same length. The image above depicts an isosceles trapezoid, ABCD. They have trapezoid and isosceles trapezoid. The segments FC and BF are congruent since the point F is the midpoint An isosceles trapezoid is a special case of trapezoid which has lateral symmetry, meaning that one side would be a mirror of the other. (image will be uploaded soon) Scalene Trapezoids A scalene trapezoid is a figure in which neither the sides nor the angles of the trapezium are equal. An image depicting an isosceles trapezoid is attached below. Let ABCD be a trapezoid with the bases AB and DC and the mid-line EF Compare the triangles DFC and FBG. In an isosceles trapezoid, the non-parallel sides of the legs of the trapezoid are equal in length.

Non isosceles trapezoid