Answer:
9. a. yes, by SSS
10. a. both ASA or AAS
Step-by-step explanation:
9. You are given two sides marked congruent and the same length for the third side, so SSS definitely applies.
In ΔABC, angle C is not marked, but is supplementary to the one marked 60°. Hence it has the same measure as angle D, marked as 120°, in ΔAED. With two known congruent angles and all three congruent sides, you can also use ASA and AAS to show congruence of the triangles.
This question does not admit multiple answers, so we should stick with the answer based on marks shown, not on deductions we can make.
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10. Together with the vertical angles, the marked angles show two of the angles of each triangle are congruent. Hence all three angles of one triangle are congruent to all three angles of the other. Together with the marked side, either ASA or AAS could be used to show congruence of the triangles.
If you don't do the extra step of showing the unmarked (non-vertical) angles congruent, you are restricted to AAS congruence. As with problem 9, there are multiple possible answers.
Since this question asks whether a given theorem can be used, I believe it should be answered considering the range of possibilities. (Your teacher may disagree, requiring AAS only.)
