`square ABCD` is a parallelogram point E is on side BC. Line DE intersects ray AB in point `T`. Prove that `DExxBE=CExxTE`.

`square ABCD` is a parallelogram point E is on side BC. Line DE inters

1.	`square ABCD` is a parallelogram point E is on side BC. Line DE intersects ray AB in point `T`. Prove that `DExxBE=CExxTE`.
Answer» `segAB\|\|segCD` …..(Opposite sides of parallelogram are parallel) i.e. set `AT\|\|` seg CD ……….`(A-B-T)` Line TD in the transversal, `:./_ATD~=/_CDT` …..(Alternate angles) i.e `/_BTE~=/_CDE……..(A-B-T,T-E-D)`..1 In `DeltaBET` and `DeltaCED` .....[From 1] `:.DeltaBET~DeltaC`........(Vertically opposite angles) `:DeltaBET~DeltaCED` ........(AA test of similarity) `:.(BE)/(CE)=(TE)/(DE)`....(Corresponding sides of similar triangles are in proportion) `:.BExxDE=CExxTE`.

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`square ABCD` is a parallelogram point E is on side BC. Line DE intersects ray AB in point `T`. Prove that `DExxBE=CExxTE`.

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