Question:In the following fig. XY is parallel to BC. Prove that the triangles ABC and AXY are similar, and hence find two expressions equal to `(XY)/(BC)`. figure Line
Answer Since XY is parallel to BC, `hat(X)=hat(B)` (corresponding). Similarly `hat(Y)=hat(C)`. The triangle `{("AXY"),("ABC"):}` are equiangular and therefore similar. `:. (XY)/(BC)=(AX)/(AB)=(AY)/(AC)` (Notice that any ratio of lengths on AB is equal to the corresponding ratio of lengths on AC. For example, `(AX)/(XB)=(AY)/(YC)`. The ratio of the transversals, XY and BC is, however, equal only to the ratio of a side of the small triangle AXY to the corresponding side of the large triangle ABC.)
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In the following fig. XY is parallel to BC. Prove that the triangles ABC and AXY are similar, and hence find two expressions equal to `(XY)/(BC)`. figure Line