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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