Triangle ABC is right angled at B and ACDE and BCGF are squares drawn on the sides AC and BC - Maths - Triangles

Question

Triangle ABC is right angled at B and ACDE and BCGF are squares
drawn on the sides AC and BC respectively Prove that (a) Traingle
BCD is congruent to triangleACG (b) GA = BD

Rajat Sethi · Accepted Answer

To Prove :(i) △ACG ≅ △BCD                  (ii) AG =BDACDE and BCGF are two squares on sides AC and BC respectively
∠ACG =∠ACB + ∠BCG=∠ACB +90°∠BCD =∠ACB + ∠ACD=∠ACB +90°Thus, ∠ACG =∠BCD
(i) In  △ACG and △BCD,we haveAC =CD (Sides of square ACDE) ∠ACG =∠BCD ( from(i) )CG =BC(Sides of square BCGF)Therefore,△ACG ≅ △BCD (By SAS rule)Thus, AG =BD(CPCT)<img alt=""
src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/tra(1)%20jpg">

Triangle ABC is right angled at B and ACDE and BCGF are squares drawn on the sides AC and BC respectively . Prove that (a) Traingle BCD is congruent to triangleACG (b) GA = BD