Q1 of 57 Page 73

In given figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.

Given,

∠A = ∠C,


AB = 6 cm, BP = 15 cm,


AP = 12 cm


CP = 4 cm


In ∆APB and ∆CPD,


∠A = ∠C [given]


∠APB = ∠CPD [vertically opposite angles]


∴ By AAA similarity criteria,


∆APD ∼ ∆CPD



By taking first two terms,



By taking first and last terms,



Hence,


length of PD = 5 cm


length of CD = 2 cm


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