Hello, geo_math!

We have a square and a rectangle .

Let be the intersection of and , the intersection of and

Prove that is parallel toCode:Q * : * * : * * : * * : * * : * θ * A : B * - - - - - * - - - - - - - - - - - * E : | * α * | * θ θ * | : | * * α | * * | : | * | * | : | * R * α | * * | : | * α * | * θ θ * | : C * - - - - - * - - - - - - - - - - - * F : * θ * D : * * : * * : * * : * * P *

Let and intersect at

Note that all angles labeled are equal.

. . And all angles labeled are 45°.

Further note that: .

In right triangles and

Hence: .

Then is an isosceles right triangle: .

Since