The Intercept Theorem

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If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.

AP || BQ || CR. The intercepts AB and BC are equal. PQ, QR are the intercepts on any other line.

PQ = QR

Through A and B draw AE and BF parallel to PQR to cut BQ and CR at E and F respectively.

To prove that PQ = QR

If P, Q, R are the mid-points of the sides AB, BC, CA respectively of the triangle ABC, prove that

(i) area of = area of

(ii) area of (area of )