Question

Determine if the two triangles are congruent. If they are, state how you know

Answer 1

Answers:

1. Congruent by SSS
2. Congruent by SAS
3. Not congruent (or not enough info to know either way)
4. Congruent by SAS
5. Congruent by SSS
6. Not congruent (or not enough info to know either way)
7. Congruent by SAS
8. Congruent by SAS

==================================

Explanations:

1. We have 3 pairs of congruent sides. The tickmarks tell us how the congruent sides pair up (eg: the double tickmarked sides are the same length). So that lets us use SSS. The shared overlapping side forms the third pair of congruent sides.
2. We have two pairs of congruent sides (the tickmarked sides and the overlapping sides), and an angle between the sides mentioned. Therefore, we can use SAS to prove the triangles congruent.
3. We don't have enough info here. So the triangles might be congruent, or they might not be. The convention is to go with "not congruent" until we have enough evidence to prove otherwise.
4. We can use SAS like with problem 2. Vertical angles are always congruent.
5. This is similar to problem 1, so we can use SSS here.
6. There isn't enough info, so it's pretty much a repeat of problem 3
7. Same idea as problem 4.
8. Similar to problem 2. We have two pairs of congruent sides and an included angle between them allowing us to use SAS

The abbreviations used were:

• SSS = side side side
• SAS = side angle side

The order is important with SAS because the angle needs to be between the sides mentioned.