Question

are or are not similar, and, if they are, state how you know. (note that figures are not to scale.)

triangle with vertices p, o, q; angle at p is 82°, angle at o is 49°

answer
attempt 2 out of 2
the triangle... because

options:
sss: three sides proportionate
sss: three sides congruent
sas: two sides proportionate, included angle congruent
sas: two sides + included angle congruent
aa: two angles congruent

Explanation:

Step1: Calculate third angle of $\triangle OPQ$

First, find $\angle Q$ using angle sum of triangles:
$\angle Q = 180^\circ - 82^\circ - 49^\circ = 49^\circ$

Step2: Identify congruent angle pairs

We now have two pairs of congruent angles:
$\angle O = \angle Q = 49^\circ$, $\angle P = 82^\circ$ (shared implicitly for similarity logic, as two angles define triangle shape)

Step3: Match to similarity criterion

Two pairs of congruent angles satisfy the AA similarity rule.

Answer:

AA: two angles congruent