By which rule are these triangles congruent?

aas
asa
sas
sss

Answer : The rule these triangles congruent are, ASA

Step-by-step explanation :

The following combinations of the congruent triangle facts  will be sufficient to prove triangles congruent.

The combinations are:

(1) SSS (side-side-side) : If three sides of a triangle are congruent to three sides of another triangle then the triangles are congruent.

(2) SAS (side-angle-side) : If two sides and included angle of a triangle are congruent to another triangle then the triangles are congruent.

(3) ASA (angle-side-angle) : If two angles and included side of a triangle are congruent to another triangle then the triangles are congruent.

(4) RHS (right angle-hypotenuse-side) : If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

As we are given two triangles.

Prove : ΔUXY ≅ ΔUVW

As,

Side YX = Side VW    (side)

∠X = ∠W                     (angle)

∠Y = ∠V                     (angle)

That means, in this two angles and a side of a triangle are equal to another triangle then the triangles are congruent.

So, ΔUXY ≅ ΔUVW         (By ASA congruency)

Hence, the rule these triangles congruent are, ASA