Question

analyzing congruence criteria
are the triangles congruent? if so, how do you know?
yes, because of asa or aas
yes, because the triangles have three congruent, corresponding angles
yes, because all the angles of the triangles are acute
not enough information given

Explanation:

Step1: Find the third angle of the first triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of the first triangle be \(x\). Then \(x + 35^{\circ}+98^{\circ}=180^{\circ}\), so \(x=180^{\circ}-(35^{\circ} + 98^{\circ})=47^{\circ}\).

Step2: Analyze congruence criteria

For the two triangles, we have two pairs of congruent angles (\(35^{\circ}\) and \(47^{\circ}\)) and a pair of congruent sides (the marked sides). This satisfies the AAS (Angle - Angle - Side) or ASA (if we consider the side - angle - side relationship with the calculated angles) congruence criteria.
The second option is wrong because having three congruent corresponding angles only makes triangles similar, not necessarily congruent. The third option is wrong as the first triangle has an obtuse angle (\(98^{\circ}\)). The fourth option is wrong as we have enough information.

Answer:

yes, because of ASA or AAS