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: Analyze angles of first triangle

In a triangle, the sum of angles is \(180^\circ\). For the first triangle, angles are \(98^\circ\), \(35^\circ\), and let the third angle be \(x\). So, \(x = 180 - 98 - 35 = 47^\circ\).

Step2: Compare angles and sides

Now, the two triangles: one has angles \(98^\circ\), \(35^\circ\), \(47^\circ\) and a marked side (indicating a congruent side), the other has angles \(47^\circ\), \(35^\circ\) and a marked side. So, we have two angles and a side (either ASA if the side is between the angles or AAS if the side is not between) congruent. So, by ASA or AAS, the triangles are congruent.

Step3: Evaluate other options

• Option 1: First triangle has a \(98^\circ\) angle (obtuse), so not all acute. Eliminate.
• Option 2: AAA (three congruent angles) does not prove congruence (only similarity). Eliminate.
• Option 4: We have angle - angle - side congruence (AAS or ASA) and a marked congruent side, so enough info. Eliminate.

Answer:

yes, because of ASA or AAS (the option: yes, because of ASA or AAS)