Question

In the above figure, seg AC and seg BD intersect each other in point P. If `("AP")/("CP") = ("BP")/("DP")`, then complete the following activity to prove ΔABP ∼ ΔCDP.

Activity: In ΔABP and ΔCDP

`("AP")/("CP") = ("BP")/("DP")` ......`square`

∴ ∠APB ≅ `square` ......Vertically opposite angles

∴ `square` ∼ ΔCDP  ....... `square` test of similarity.

Answer 1

In ΔABP and ΔCDP,

`("AP")/("CP") = ("BP")/("DP")` ......Given

∴ ∠APB ≅ ∠CPD ......Vertically opposite angles

∴ ΔABP ∼ ΔCDP  ....... SAS test of similarity.