91Ó°ÊÓ

The labelled diagram satisfying the given statement is:

The statement is: If pentagon$ABCDE$ is equilateral and has right angles at and , then diagonals$\stackrel{¯}{AC}$ and$\stackrel{¯}{AD}$ form congruent triangles.

As, pentagon$ABCDE$ is equilateral.

Therefore, by using the definition of equilateral it can be said that $AB=BC=CD=DE=EA$.

That implies, $ABâ‰\dots BCâ‰\dots CDâ‰\dots DEâ‰\dots EA$.

Therefore, it is given that $AB=BC=CD=DE=EA$.

As, the pentagon has right angles at$B$ and $C$.

Therefore,$∠B=∠E=90°$

Therefore, it is given that $∠B=∠E=90°$.

As the triangles formed are to be proved congruent and the triangles formed are $â–³ABC$and $â–³AED$.

Therefore, it is to be proved that $â–³ABCâ‰\dots â–³AED$.

In the triangles $△ABC$and $△AED$, it can be seen that $AB=AE$, localid="1648808792083" $∠B=∠E=90°$and $BC=ED$.

Therefore, the triangles $â–³ABC$and$â–³AED$are the congruent triangles by using the SAS postulate

The proof in two-column form is: