Determine whether or not two triangles in each pair are congruent. If they are congruent, show your reasoning in your flow chart. If the triangles are not congruent or you cannot determine they are, justify your conclusion.

a.

SAS stands for "side angle side". The "side" refers to one pair of sides, so we have two pairs of sides overall. The "angle" refers to a pair of angles.

Let's break down the SAS in more detail...

b.

ASA = angle side angle

More detailed breakdown:

c.

We don't have enough info to say whether the triangles are congruent or not. Since we cannot say they are congruent, we side with the fact that they aren't congruent.

We have a pair of sides (BI = BL and BT = BT) and a pair of angles (angle TIB = angle TLB) so it seems like we have enough info since you might be thinking of SAS. However, we cannot use SAS because the angles mentioned are not between the sides mentioned. Angle TIB is not between side IB and side BT.

Side note: if we knew that BT was perpendicular to IL, then we could use the hypotenuse leg theorem to prove the triangles to be congruent.

d.

The sides mentioned are not between the angles. Though if we involved both pairs of alternate interior angles, then we could use ASA

Now the sides are between the congruent angles.

So you have a choice between using AAS or ASA. Either theorem would work.

Side note: if you know two angles in a triangle, then you could solve for the third one using the idea that x+y+z = 180, where x,y,z are the three angles of a triangle. This is why AAS and ASA are closely linked. In this case, we didn't have to do this because we already know the three pairs of corresponding angles are congruent through other means.

step-by-step explanation: