Question

determine if triangle $ghi$ and triangle $jkl$ are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles
✓ similar.

Explanation:

Step1: Find missing angle in △GHI

Sum of angles in triangle is $180^\circ$.
$\angle H = 180^\circ - 86^\circ - 55^\circ = 39^\circ$

Step2: Check corresponding angles

In △JKL, $\angle L = 86^\circ$ (matches $\angle I$ in △GHI). Now check side ratios:
$\frac{GI}{JL} = \frac{16}{32} = \frac{1}{2}$, $\frac{IH}{LK} = \frac{21}{42} = \frac{1}{2}$

Step3: Verify SAS similarity

The included angles of the proportional sides are equal ($\angle I = \angle L = 86^\circ$), and the adjacent sides are in equal ratio.

Answer:

The triangles are similar, by the Side-Angle-Side (SAS) Similarity Criterion.