Which congruence theorem would complete the proof shown? SSS SAS ASA

Answer : ASA congruence theorem would complete the proof shown.

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 : ΔDAC ≅ ΔBAC

As,

Side CA = Side CA    (side)

∠2 = ∠3                     (angle)

∠1 = ∠4                      (angle)

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

So, ΔDAC ≅ ΔBAC    (by ASA rule)

Hence, ASA congruence theorem would complete the proof shown.

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