Ex 6.5

Ex 6.5, 1
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Chapter 6 Class 10 Triangles

Serial order wise

Last updated at May 29, 2018 by Teachoo

Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC ā„ BD. Show that AB2 = BC . BD Given: ABD is a triangle right angled at A . & AC ā„ šµš· To prove: AB2 = BC . BD i.e. š“šµ/šµš· = šµš¶/š“šµ Proof: From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, Ī BAD ā¼ Ī ACB If two triangles are similar , then the ratio of their corresponding sides are equal šµš“/šµš¶=šµš·/šµš“ BA Ć BA = BD Ć BC BA2 = BD Ć BC i.e. AB2 = BD Ć BC Hence proved Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC ā„BD. Show that (ii) AC2 = BC . DC We need to prove: AC2 = BC . DC i.e. š“š¶/š·š¶ = šµš¶/š“š¶ From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, Ī BCA ā¼ Ī ACD If two triangles are similar , then the ratio of their corresponding sides are equal šµš¶/š“š¶=š¶š“/š¶š· BC Ć CD = AC Ć CA BC Ć CD = AC2 AC2 = BC Ć CD Hence proved Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC ā„BD. Show that (iii) AD2 = BD . CD We need to prove: AD2 = BD . CD i.e. š“š·/š¶š· = šµš·/š“š· From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, Ī DAB ā¼ Ī DCA If two triangles are similar , then the ratio of their corresponding sides are equal š·š“/š·š¶=š·šµ/š·š“ DA Ć DA = DB Ć DC DA2 = DB Ć DC AD2 = BD Ć CD Hence proved