In the following figure. E is a point on side CB produced of an isosce

1.	In the following figure. E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ABD ~ ∆ECF
Answer» Data: E Is a point on side CB produced of an isosceles ∆ABC with AB = AC. AD ⊥ BC and EF ⊥ AC, To Prove: ∆ABD ~ ∆ECF In ∆ABD and ∆ECF. ∠ADB = ∠EFC = 90° (data) ∠ABD = ∠FCE (∵ ∠B = ∠C) ∠BAD = ∠FEC ∴ Equiangular triangles. ∴ Similarity criterion for triangles is A.A.A. ∴ ∆ABD ~ ∆ECF.

In the following figure. E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ABD ~ ∆ECF

Answer»

Data: E Is a point on side CB produced of an isosceles ∆ABC with AB = AC. AD ⊥ BC and EF ⊥ AC,

To Prove: ∆ABD ~ ∆ECF

In ∆ABD and ∆ECF.

∠ADB = ∠EFC = 90° (data)

∠ABD = ∠FCE (∵ ∠B = ∠C)

∠BAD = ∠FEC

∴ Equiangular triangles.

∴ Similarity criterion for triangles is A.A.A.

∴ ∆ABD ~ ∆ECF.