F
E or C (depending on the actual angles - see below in the details)
Step-by-step explanation:
two triangles are congruent, when after some rotation or mirroring they can cover each other exactly.
that means they must both have the same angles and side lengths.
these are the possible conditions to determine that 2 triangles are congruent (without knowing ALL of the sides and angles) :
SSS (Side-Side-Side) - all 3 sides of triangle 1 are exactly of the same length as the 3 sides of triangle 2.
SAS (Side-Angle-Side) - 2 sides and one angle are the same
ASA (Angle-Side-Angle) - 2 angles and the side between these 2 angles are the same
AAS (Angle-Angle-Side) - 2 angles and any not-included side are the same
RHS (Right angle-Hypotenuse-Side) - both triangles are right-angled (one angle is 90 degrees), and the Hypotenuse (the side opposite to the 90 degree angle) and another side are the same.
so, now look at a).
we only know the angles. but we could use a zoom lens of a camera and make them bigger and smaller, while their angles remain actually the same.
therefore, we cannot say, if they are actually congruent (only if their side lengths are the same too).
but we can say that they could be congruent.
and therefore also none of the congruent conditions apply, because for all of them we always need at least one side length. and we don't have that.
now looking at b)
I am not sure I can read one of the given angles correctly.
case one: I read the angles in triangle 2 as 66 and 58 degrees. that would make the third angle
180 - 66 - 58 = 56
but triangle 1 has the angles of 68, 54 and
180 - 68 - 54 = 58
=> the three angles are not the same, so the triangles are definitely not congruent
case two: I could read the angles in triangle 2 also as 68 and 58. that would make the third angle
180 - 68 - 58 = 54
and the side connecting the 68 and 58 angles has the same length, so the ASA criteria are fulfilled, and the triangles are congruent. C
