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Problems on Equal Intercepts Theorem

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

1. 

Problems on Equal Intercepts Theorem

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.

Problems on Equal Intercepts

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.






9th Grade Math

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