Are these congruent triangles ?? (1 Viewer)

[Drewk]

Really weird question in grove textbook are the triangles in the picture congruent ??
The book's answers says they are NOT
Please explain

 

[BL3H]

From what's given we can't say they're congruent.

We have two sides and an angle equal.

BUT we need:
Angle Angle Side
Side Angle Side
Side Side Side
Or
Right angle Hypotenuse Side

 

[BL3H]

In and :
AC = EF (given)
BC = DF (given)


From this we cannot conclude ABC is congruent to EDF due to not being able to fulfil the rules above.

 

[Carrotsticks]

I think what BL3H is trying to say is that although we do satisfy the "SAS" Criteria, the angle is NOT in between the two sides.

For SAS to be satisfied, we must have two sides, and the angle MUST be coming from those 2 sides as follows:

Since we don't have that here, we can't conclude that the two triangles are congruent. The reason is because of the "Ambiguous Case" of the Sine Rule, which arises from the identity sin(180-x) = sin(x).

 

[BL3H]

I think what BL3H is trying to say is that although we do satisfy the "SAS" Criteria, the angle is NOT in between the two sides.

For SAS to be satisfied, we must have two sides, and the angle MUST be coming from those 2 sides as follows:

Since we don't have that here, we can't conclude that the two triangles are congruent. The reason is because of the "Ambiguous Case" of the Sine Rule, which arises from the identity sin(180-x) = sin(x).

yeah dat.

I would also do the cosine/sine rule to check if the angles were equal but cbf.