**picture provided** how is ars isosceles?

Check the picture below.

since the trapezoid is an isosceles trapezoid, namely segments VR = TS, the segment TR will be the same length as the segment VS, those diagonals.

in an isosceles trapezoid, you have the bases, the parallel sides, and the legs, the legs are the same length and they can only be arranged in a way that both will produce the same angles on either end.

that means the angle made at TRV(lower-left-corner), is equals to the angle made at VST(lower-right-corner).

so, we know that because the trapezoid is an isosceles one, VR = TS, and for the same angle constraints we know that ∡TRV = ∡VST, so that angle and that side are the same for both triangles.

now, let's look at the vertex A, the vertex A is a junction for the two diagonals, and at a junction of two lines, you have a "vertical angle" on either side, and vertical angles are always equal, since they're just across from each other on a junction.

so each triangle has an Angle, then another Angle, and then a Side, but the side is not between the angles, is outside.  Thus both of those triangles are congruent by AAS, Angle Angle Side.

because those two triangles are congruent by AAS, that means the segments AR = AS, and if those two segments are just twins, that means the ∡ARS has those twins, and a triangle with twin sides is an isosceles.