Q2 of 42 Page 220

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively.

Prove that AE2 + CD2 = AC2 + DE2 .


Given, ABC as a right angled triangle


Need to prove that AE2 + CD2 = AC2 + DE2


⇒ In right angled triangle ABC and DBC, we have


⇒ AE2 = AB2 + BE2 ………..eq(1)


⇒ DC2 = DB2 + BC2 ……….eq(2)


⇒ Adding equation 1 and 2 we have


⇒ AE2 + DC2 = AB2 + BE2 + DB2 + BC2


= (AB2 + BC2) + (BE2 + DB2)


⇒ Since AB2 + BC2 = AC2 in right angled triangle ABC


∴ AC2 + DE2


Hence proved


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