Question

analyzing congruence criteria
are the triangles congruent? if so, how do you know?
two triangles with angle and side markings
options:
not enough information given
yes, because the triangles have three congruent corresponding angles
yes, because of asa or aas
yes, because all the angles of the triangles are acute

Explanation:

Step1: Analyze triangle angles

First, calculate the third angle of the left triangle. The sum of angles in a triangle is \(180^\circ\). So, \(180 - 47 - 35 = 98^\circ\). The right triangle has angles \(35^\circ\), \(98^\circ\), and \(180 - 35 - 98 = 47^\circ\). So both triangles have angles \(35^\circ\), \(47^\circ\), \(98^\circ\), and a pair of marked (congruent) sides.

Step2: Identify congruence criterion

We have two angles and a side (AAS or ASA). The marked side is between angles? Wait, no: in left triangle, angles \(47^\circ\), \(35^\circ\) with the side between? Wait, the left triangle has angles \(47^\circ\), \(35^\circ\), and the side with the mark; the right triangle has \(35^\circ\), \(98^\circ\), and the marked side. Wait, actually, both triangles have angles \(35^\circ\), and a side (marked) and another angle (left: \(47^\circ\), right: \(98^\circ\)? Wait no, earlier calculation: left triangle angles: \(47^\circ\), \(35^\circ\), \(98^\circ\); right triangle: \(35^\circ\), \(98^\circ\), \(47^\circ\). So the marked side is a side that is adjacent to \(35^\circ\) and another angle. So we have two angles and a non - included side (AAS) or included? Wait, actually, since we have two angles and a side (the marked one) that is congruent, and the angles are corresponding, so by AAS (Angle - Angle - Side) or ASA (Angle - Side - Angle) congruence criterion, the triangles are congruent. So the correct option is the one that says "yes, because of ASA or AAS".

Answer:

The option "yes, because of ASA or AAS" (the bottom - right option among the four cards).