91Ó°ÊÓ

The labelled diagram satisfying the given statement is:

The statement is: In an isosceles triangle, if the angle between the congruent sides is bisected, then two congruent triangles are formed.

Consider a triangle $ABC$.

As, the triangle$ABC$ is an isosceles triangle, therefore the two sides of the triangle are equal.

Consider the two equal sides$AC$ be and $AB$.

That implies, $ACâ‰\dots AB$.

Therefore, it is given that $AC=AB$.

As, the angle between the congruent sides is bisected.

That implies the angle$CAB$ is bisected.

Therefore, by using the definition of angle bisector, it can be said that$∠CAD=∠BAD$

That implies, $∠CADâ‰\dots ∠BAD$.

Therefore, it is given that $∠CAD=∠BAD$.

As, the triangles formed are to be proved congruent and the triangles formed are$â–³ADC$ and $â–³ADB$.

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

In the triangles$â–³ADC$ and $â–³ADB$, it can be noticed that$AD=AD$ by using the reflexive property.

That implies, $ADâ‰\dots AD$.

Therefore, it can be seen that $AC=AB$, $∠CAD=∠BAD$and $AD=AD$.

Therefore, the triangles$â–³ADC$ and$â–³ADB$ are the congruent triangles by using the SAS postulate.

The proof in two-column form is: