Question

PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!

Answer 1

2, 3, 4, 7, 8, 10 I hope

Answer 2

Answers

1. Congruent by AAS (shown in the example)
2. Congruent by SAS
3. Congruent by SSS
4. Congruent by ASA
5. Not enough info (shown in the second example)
6. Congruent by AAS
7. Congruent by SAS
8. Congruent by SSS
9. Congruent by AAS
10. Not congruent

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Explanations:

1. As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.
2. We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.
3. We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.
4. Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.
5. We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.
6. As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).
7. This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.
8. This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.
9. The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).
10. For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).

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Acronyms

SSS = side side side

SAS = side angle side

ASA = angle side angle

AAS = angle angle side