Answer:
PG ≅ SG (Given)
PT ≅ ST (Given)
GT = GT (Common)
∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)
Explanation:
Given: PG ≅ SG and PT ≅ ST
To Prove: ∠GPT ≅ ∠GST
Proof: PG ≅ SG (Given)
PT ≅ ST (Given)
GT = GT (Common)
∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).
SSS Congruency Axiom: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
Congruence: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.