Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?

Question

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a. AAS only
b. ASA only
c. either ASA or AAS
d. neither

Answer 1

c. either ASA or AAS

You know the top and bottom horizontal lines are parallel (because of the right angles they form with the center verticle line), which makes the top left and bottom right angles equal (alternate angles). You can now use the AAS theorem since two angles and a side are equal.

Alternatively, you can then calculate the third angle (in the middle) for both triangles, giving you access to the ASA postulate.

Answer 2

Both. Clearly, you are given one pair of side lengths congruent and one pair of angles congruent. But you can still there is a second pair of angles which are congruent because they are vertical angles. Certainly, then by AAS Theorem, the triangles are congruent. But since these two triangles have two pairs of angles congruent, this implies that the third pair must also be congruent. Then we could use ASA Postulate to say the two triangles are congruent. Both ASA and AAS.

Answer 3

c. either ASA or AAS
If two angles are equal, the third angles must also be equal. Hence AAS and ASA are the same

Answer 4

C. either ASA or AAS

Answer 5

We totally just learned this in geometry. B!