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

Question

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

Rashi Lokwani · Accepted Answer

Dear Student,

∠DCA = 90° (Since ACDE is a square)∠GCB = 90° (Since ACDE is a square)Now, ∠BCD = ∠DCA + ∠ACB⇒∠BCD = 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

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

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