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