Math Help - Inequality Proof

1. Inequality Proof

Please solve the attached proof.

2. Hello jwpaul

Welcome to Math Help Forum!

Sorry, but this question doesn't make sense.

If $\angle1 \cong \angle 2$, then $\triangle ETS$ is isosceles, with $ET = TS$.

Similarly $\triangle PAT$ is isosceles, with $PT = TA$.

Then $PS = PT+TS = AT + TE = AE$.