If in a two triangles corresponding angles are equal then their corresponding sides are in same ratio hence two triangle are similar
Shaalaa.com | Similar Triangles Theorem
O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in
F, D and E respectively.
BF × AE × CD = AF × CE × BD
In the given figure, X is any point in the interior of triangle. Point X is joined to vertices of triangle. Seg PQ || seg DE, seg QR || seg EF. Fill in the blanks to prove that, seg PR || seg DF.
Proof : In Δ XDE, PQ || DE ........ ___________
`therefore "XP"/([ ]) = ([ ])/"QE"` ..... (I) (Basic proportionality theorem)
In Δ XEE, QR || EF ........ _________
`therefore ([ ])/([ ]) = ([ ])/([ ])` .......(II) _________________
`therefore ([ ])/([ ]) = ([ ])/([ ])` ....... from (I) and (II)
∴ seg PR || seg DE ........... (converse of basic proportionality theorem)
If ΔABC ~ ΔDEF, then writes the corresponding congruent angles and also write the ratio of corresponding sides.