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| 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. |
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| AP || BQ || CR. The intercepts AB and BC are equal. PQ, QR are the intercepts on any other line. |
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| PQ = QR |
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| Through A and B draw AE and BF parallel to PQR to cut BQ and CR at E and F respectively. |
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| To prove that PQ = QR |
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| If P, Q, R are the mid-points of the sides AB, BC, CA respectively of the triangle ABC, prove that |
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(i) area of  = area of  |
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(ii) area of  (area of  ) |
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