Question

which rule explains why these triangles are similar?
sss
sas
aa
none of the above; the triangles cannot be proven similar
write a similarity statement.
△ijh ~ △fed

Explanation:

Step1: Find missing angle in △IJH

The sum of angles in a triangle is $180^\circ$.
$\angle I = 180^\circ - 80^\circ - 56^\circ = 44^\circ$

Step2: Find missing angle in △FED

The sum of angles in a triangle is $180^\circ$.
$\angle F = 180^\circ - 80^\circ - 63^\circ = 37^\circ$

Step3: Match congruent angles

$\angle H = \angle D = 80^\circ$. No other pairs of angles are equal, so AA (Angle-Angle) similarity does not apply, and no side information is given for SSS/SAS.

Step4: Evaluate similarity rule

Since only one pair of angles is congruent, the triangles cannot be proven similar with the given rules.

Answer:

1. Correct option: none of the above; the triangles cannot be proven similar
2. The triangles cannot be proven similar, so no valid similarity statement exists.