Determine if the 2 triangles are congruent. if so how do you know?

C)

Step-by-step explanation:

Two triangles are considered congruent if they are essentially the same triangle. In geometry, we have 4 different tests to check whether or not two triangles are the same.

1) SSS -- Three sides are equal in magnitude in the same orientation. The way this works is that, if all three sides are the same in the same order, then the angles in between the sides are essentially the same. So, by nature, they are similar since one triangle can be scaled to match another triangle. But not only that, in fact, the scale factor is 1. So they are congruent.

2) SAS -- Two sides are equal in magnitude and the angle formed in between the two sides are equal. In much the same way, that means every other angle must be equal in two triangles. And hence, we have congruency.

3) AAS -- Two angles and a side is equal.

4) RHS/HL -- It is known that the hypotenuse, a side, and the right angle are equal. This is a special case of the "SAS" rule.

With the four proofs highlighted, we will now try to deduce whether or not these triangles are indeed congruent.

1) doesn't work because we are not given all three sides.

2) works (since vertically opposite angles are indeed equal)

3) doesn't work.

4) works.

So, out of the four options, (C) seems to be the most correct (by theorem 4)

step-by-step explanation:

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