Question

Prove the ASA theorem. Pls I dont get the ncert version thank you guys.

Answer 1

Given: triangle ABC and triangle DEF with angle A congruent to angle D, angle C congruent to angle F, and side AC congruent to side DF

Prove: triangle ABC is congruent to triangle DEF

 

Proof: By congruence axiom 1, there is a unique point X on DE such that AB is congruent to DX.  By hypothesis, angle A is congruent to angle D and AC is congruent to DF, so triangle ABC is congruent to triangle DXF by SAS.  By the definition of congruent triangles, angle C is congruent to angle DFX.  By hypothesis, angle C is congruent to angle DFE, so by the uniqueness of congruence axiom 4, FE is congruent to FX.  So, E = X. Hence, triangle ABC is congruent to triangle DEF.