Question

In the given figure, seg AC and seg BD intersect each other in point P and `"AP"/"CP" = "BP"/"DP"`. Prove that, ∆ABP ~ ∆CDP.

Answer 1

Given: Seg AC and seg BD intersect each other in point P and `"AP"/"CP" = "BP"/"DP"`.

To prove: ∆ABP ~ ∆CDP

Proof: In ∆ABP and ∆CDP,

`"AP"/"CP" = "BP"/"DP"`   ...(Given)

∠APB ≅ ∠CPD       ...(vertically opposite angles)

By SAS test of similarity,

∆ABP ~ ∆CDP 

Hence Proved.