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

From Problems on Equal Intercepts Theorem to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?