Answer:
No
Step-by-step explanation:
You want to know if there is enough information to claim ∆PQT ≅ ∆SRT by the HL theorem.
HL theorem
The HL theorem tells you right triangles are congruent if they have one leg (L) and the hypotenuse (H) congruent.
Here, the triangles are not indicated as being right triangles, so the HL theorem cannot be applied.
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Additional comment
There is not enough information here to permit the triangles to be declared congruent.
For congruence by any theorem, we'd need to know that angle T is the largest angle in each triangle, a condition not supported by the evidence.
Though rarely (if ever) seen in congruence discussions, a claim of SSA congruence can only be supported if the angle (A) is opposite the longest side. When the angle is 90°, this is called the HL congruence theorem. When the angle is known to be obtuse, it will always be opposite the longest side.
When the given angle is opposite the shortest of the two given sides, there are two possible triangles that can be constructed. Hence congruence cannot be guaranteed between two triangles with the same SSA dimensions.
