Question

In the figure, D is a point on the side BC of ∆ABC such that ∠ADC = ∠BAC Prove that CA / CD = CB/ CA

Answer 1

Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

•Similarity of triangles should be expressed symbolically using correct correspondence of their vertices
AA similarity: if two angles of one triangle are respectively equal to two angles of another triangle then the two Triangles are similar.

SOLUTION:

In  ΔABC & ΔDAC
∠ADC = ∠BAC                 [Given]
∠ACB = ∠DCA             [Common angle]
ΔABC  ~ ΔDAC (By AA similarity criterion)
AC/DC =CB/CA

or
CA/ CD= CB/CA
[corresponding sides of two similar triangles are proportional]

Hence, proved.

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