Condition for Congruent Triangles

If their sides are equal to each other in the two right-angled isosceles triangles given, then $\angle A=\angle E$. 

In the two right-angled isosceles triangles, prove that $\angle B=\angle E$ if their sides (other than the hypotenuse) are equal to each other?

In the two right-angled isosceles triangles, prove that $AB=DE$ if their sides (other than the hypotenuse) are equal to each other?

Prove that any two right-angled isosceles triangles are congruent if their sides are equal to each other?

What is congruence among the right-angled isosceles triangles?

In the given pair of triangles, parts bearing identical marks are congruent. State the test by which triangles are congruent. $RHS/SSS/SAS/ASA$

In the given pair of triangles, parts bearing identical marks are congruent. State the corresponding vertex to $X$.

In the given pair of triangles, parts bearing identical marks are congruent. The condition by which the triangles are congruent is $\mathrm{RHS}$.

State True or False:

Two equilateral triangles are always congruent.

Sheela drew a triangle whose dimensions were x cm, y cm and z cm.

Meena drew a triangle whose dimensions were exactly half that of Sheela’ triangle.

Leela said both triangles followed the SSS rule of congruency as they were exactly proportional.

Reena pointed out that they were similar and not congruent.

Tina gave a solution to make the triangles congruent.

Pick the right option.

Which value of x will prove ∆ ABC ≌ ∆ DEF by SSS postulate?

Martha outlined the shape of a triangle where side PQ and side PR measure 4 ft each. If S is the midpoint of QR, is ∆ PQS ≌ ∆PRS?

In ∆ PQR and ∆ PSR, PQ = PS and QR = SR. What is a third criterion so that the two triangles are congruent?

If we prove ∆ XYZ ≌ ∆ PQR by SSS congruence rule that means:

Is ∆ADB $ ≌$ ∆CDB?

The three sides of ∆HAT are equal to the sides of ∆RSI. Are the two triangles congruent?

The triangles are congruent due to which postulate?

In ∆ABC and ∆EFG, AB = EF, BC = FG. If ∆ ABC ≌ ∆EFG according to SAS rule of congruency then the necessary criteria that must be true in the figures to prove the congruency is

To find the measure of angle A, identify the steps to be followed.