Question

Given: DC||AB DC = AB

Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. If it is not possible to prove the triangles are congruent, choose "not possible".

SSS
SAS
ASA
not possible

Answer 1

SAS

Explanation:

Given,

DC || AB,

DC = AB

We have to prove that : triangles shown in the diagram are congruent.

Proof :

Since, in triangles ADC and ABC,

AC ≅ AC ( common segments ),

DC || AB

⇒ ∠DAC ≅ ∠ ACB ( By alternate interior angle theorem )

DC = AB ( given )

Hence, By SAS ( side - angle - side ) postulate of congruence,

Δ ADC ≅ Δ CAB,

Second option is correct.