# Problems on Equal Intercepts Theorem

Here we will solve different types of problems on Equal Intercepts Theorem.

1.

In the above figure, MN ∥ KL ∥ GH and PQ = QR. If ST = 2.2 cm, find SU.

Solution:

The transversal PR makes equal intercepts, PQ and QR, on the three parallel lines MN, KL and GH.

Therefore, by the Equal Intercepts Theorem, ST = TU = 2.2 cm.

Therefore, SU = ST + TU = 2.2 cm + 2.2 cm = 4.4 cm.

2. In a quadrilateral JKLM, JK ∥ LM. A line parallel to LM is drawn through the midpoint X of KL, which meets JM at Y. Prove that XY bisects JM.

Solution:

Given: In the quadrilateral JKLM, JK ∥ LM. X is the midpoint of KL and XY ∥ LM.

To prove: XY bisects JM.

Proof:

 Statement Reason 1. JK ∥ LM ∥ XY. 1. JK ∥ LM and XY ∥ LM. 2. KL makes equal intercepts on JK, XY and LM. 2. Given that KX = XL. 3. JM also makes equal intercepts on JK, XY and LM. 3. By the Equal Intercepts Theorem. 4. JY = YM. 5. From statement 3. 5. XY bisects JM. (Proved). 5. From statement 4.

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