Question

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

Explanation:

Step1: Calculate the third angle of the first triangle

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

Step2: Analyze congruence criteria

For triangles to be congruent, we need information about side - side - side (SSS), side - angle - side (SAS), angle - side - angle (ASA), or angle - angle - side (AAS) congruence. Here, we only have information about angles. Just having three congruent corresponding angles (which we have, since both triangles have angles \(35^{\circ},47^{\circ},98^{\circ}\)) is not sufficient for congruence. It is the criterion for similarity (by AA similarity, since if two angles of one triangle are equal to two angles of another triangle, the third angle is also equal as the sum of angles in a triangle is \(180^{\circ}\)). But for congruence, we need at least one pair of corresponding sides to be equal.

Answer:

not enough information given