Answer:
ASA
Step-by-step explanation:
ASA stands for Angle-Side-Angle which is the congruency theorem that states that if a triangle shares two congruent angles that have one line in between the two angles share a side length congruent to each other, then the two triangles are congruent.
Before you get very confused on the difference between AAS (Angle-Angle-Side) and ASA (Angle-Side-Angle), let explain why these two triangles are ASA.
We are given that both triangles share a similar side length at KL where they are connected. We are also given that angle ∠JKL is congruent to angle ∠MKL. We are also given that angle ∠MLK is congruent to angle ∠JLK.
The most important part after deciding all the relationships is given to us, it is deciding what kind of congruence theorem we will use. We are given the options:
- SSS (Side-Side-Side)
- SAS (Side-Angle-Side)
- ASA (Angle-Side-Angle)
- AAS (Angle-Angle-Side)
- HL (Hypotenuse-Leg)
Because we are presented with two congruent angles and one congruent side, we know that this triangle congruency theorem is either ASA or AAS. To understand why these triangles are ASA, we have to look at where the two-given congruent sides are located. As we can see in the name and in our two triangles, the congruent side lengths are in between the two angles as it touches both angle ∠JKL and angle ∠JLK in triangle ΔJKL, while in on ΔMKL, the congruent side length is also found between angle ∠MLK and angle ∠MKL. So, these triangles share ASA because they share two congruent angles connected by one congruent line.
ORDER MATTERS WHEN YOU WRITE YOUR CONGRUENCY THEROMS
AAS is technically not the same as ASA and I will explain that in one moment.
An example of AAS is if instead being told that ∠JKL is congruent to angle ∠MKL, we are given that ∠KJL is congruent to angle ∠KML instead. now the congruent sides are not connected to angle ∠KJL or angle ∠KML. The side is no longer in-between the two congruent sides. The reason order matters here are because order matters between AAS and ASA because in another theorem, SAS, you will find out order matter because while SAS guaranties congruency SSA does not. Technically, though, while both AAS and ASA both guaranty congruency, they are labeled separately, the way the remaining congruency thermos are.
