Hello, sanee66!

In quadrilateral MNOA, triangles PNO and PMA are congruent

and APO is an isosceles triangle.

Prove that MNOA is an isosceles triangle.Code:P M * - - - - * - - - - * N / β * * β \ / * * \ / * * \ / * * \ / * α α * \ A * - - - - - - - - - - - - - - - * O

Since

. . So we must prove that: .

Since

. . Let

We note that: . .[1]

Since is isosceles,

. . Let

In

Substitute into [1]: .

Hence: . .(alternate-interior angles)

Therefore, is an isosceles trapezoid.