D is a point on side BC of - ABC such that angle ADC - angle BAC- prove that CA - CD - CB - CA-

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Standard X

Mathematics

Basic Proportionality Theorem

D is a point ...

Question

D is a point on side BC of ΔABC such that angle ADC = angle BAC. prove that CA/CD=CB/CA.

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Solution

In ΔABC and Δ ADC

∠BAC = ∠ADC (given)
∠ACB = ∠DCA (common)
therefore ∠ABC = ∠CAD
Hence Δ ABC and Δ DCA are similar
So, Ratio of their corresponding sides are equal

therefore CA/CB = CD/CA
or CA/CD = CB/CA proved

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D is a point on side BC of ΔABC such that angle ADC = angle BAC. prove that CA/CD=CB/CA.

In ΔABC and Δ ADC ∠BAC = ∠ADC (given) ∠ACB = ∠DCA (common) therefore ∠ABC = ∠CAD Hence Δ ABC and Δ DCA are similar So, Ratio of their corresponding sides are equal therefore CA/CB = CD/CA or CA/CD = CB/CA proved

In ΔABC and Δ ADC

∠BAC = ∠ADC (given)
∠ACB = ∠DCA (common)
therefore ∠ABC = ∠CAD
Hence Δ ABC and Δ DCA are similar
So, Ratio of their corresponding sides are equal

therefore CA/CB = CD/CA
or CA/CD = CB/CA proved