Question

In the following figure, ABC and AMP are two right triangles, right-angled at B and M, respectively. Prove that: 

(i) ΔABC ~ ΔAMP 
(ii) \(\frac{CA}{PA}=\frac{BC}{MP}\)

Answer 1

1. In ∆ABC and ∆AMP, 
   \(\angle\)ABC = \(\angle\)AMP (Each 90°)
   \(\angle\)A = \(\angle\)A (Common)
   ∴ ∆ABC ∼ ∆AMP (By AA similarity criterion)
2. \(\Rightarrow\frac{CA}{PA}=\frac{BC}{MP}\)