In given figure triangle ABC is right angled at B. ACDE & BCGF are squares. Prove
(i) triangle BCD is congruent to triangle ACG
(ii)AG =BD



Dear Student,

DCA = 90° (Since ACDE is a square)GCB = 90° (Since ACDE is a square)Now, BCD = DCA + ACBBCD = 90° + ACB   ....(1)And,GCA = GCB + ACB  GCA = 90° + ACB   ....(2) From (1) and (2)BCD = GCAIn BCD and GCA,CD = CA (Sides of the same square)BCD = GCA (Proved above)GC = BC (Sides of the same square)Hence,BCD  GCA, By SAS congruence criterion.Also, DB= AG by CPCT

Regards

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