Answer:
ASA postulate
Step-by-step explanation:
The sum of the measures of interior angles of triangle is always 180°, so
∠LRT=180°-∠RTL-∠RLT=180°-∠2-∠4;
∠KST=180°-∠STK-∠SKT=180°-∠1-∠3.
Since
∠1≅∠2 and ∠3≅∠4, we have that ∠LRT ≅ ∠KST.
The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. (The included side is the side between the vertices of the two angles.)
In your case:
- ∠1 ≅ ∠2;
- ∠LRT ≅ ∠KST;
- TS ≅ TR (included sides)
Triangles TKS and TLR are congruent by ASA postulate.
