Could someone please help me prove that this is an isosceles trapezoid? Thank you in advance.
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.