In the quadrilateral ABCD, ab = DC, m and N are the midpoint of AD and BC, and GH is vertical to Mn, intersect AB and CD at point G respectively, and verify: ∠ AGH = ∠ DHG First, in the first row, are triangles similar?

In the quadrilateral ABCD, ab = DC, m and N are the midpoint of AD and BC, and GH is vertical to Mn, intersect AB and CD at point G respectively, and verify: ∠ AGH = ∠ DHG First, in the first row, are triangles similar?

Connecting an and DN, the two sides of the triangle ABN, DCN, BN = CN, ab = DC are proportional respectively. If the triangle is similar, the angle B = angle c can be obtained. Similarly, connecting BM and cm
The intersection of Mn and GH is o,
In the quadrilateral ABCD, angle a + angle B + angle c + angle d = 360
So angle a + angle B = 180, angle c + angle d = 180
So ad / / BC, in the isosceles trapezoid ABCD, if n passes through point AB CD and parallel lines intersect ad at P, Q, there will be parallelogram abnp, cdqn, NP = NQ, AP = DQ, PM = am-ap, MQ = md-qd, PM = MQ, three sides are equal, triangle is congruent, angle amn = angle MND = 90, ad is vertical Mn, then we can use both vertical and quadrilateral inner angles to be equal