Q3 of 49 Page 151

Two triangles ABC and DBC have common base BC. Suppose AB = DC and ∠ABC = ∠BCD. Prove that AC = BD.


In ΔABC and ΔDBC


BC = BC … common side


∠ABC = ∠DBC … given


AB = CD … given


Therefore, by SAS test for congruency


ΔABC ≅ ΔDCB


⇒ AC = BD … corresponding sides of congruent triangles


Hence proved AC = BD


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