# Equal Intercepts Theorem

Intercept

In the figure given above, XY is a transversal cutting the line L1 and L2 at P and Q respectively. The line segment PQ is called the intercept made on the transversal XY by the lines L1 and L2.

If a transversal makes equal intercepts on three or more parallel lines then any other transversal cutting them will also make equal intercepts.

Given: Let there be three straight lines L1, L2, and L3 such that L1 ∥ L2 ∥ L3.

Transversal AB makes equal intercepts on L1, L2 and L3, I.e., PQ = QR. Another transversal CD makes intercepts KM and MN.

To Prove: KM = MN.

Construction: Join PN which cuts the L2 at O.

Proof:

 Statement Reason 1. PQ = QR and QO ∥ line L3. 1. Given. 2. O is the midpoint of PN, i.e., PO = ON. 2. By converse of Midpoint Theorem. 3. PO = ON and OM ∥ L1. 3. By statement 2 and given. 4. M is the midpoint of NK, i.e., KM = MN (Proved) 4. By converse of Midpoint Theorem.

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.

## Recent Articles

1. ### Constructing a Line Segment |Construction of Line Segment|Constructing

Aug 14, 24 09:52 AM

We will discuss here about constructing a line segment. We know how to draw a line segment of a certain length. Suppose we want to draw a line segment of 4.5 cm length.

2. ### Construction of Perpendicular Lines by Using a Protractor, Set-square

Aug 14, 24 02:39 AM

Construction of perpendicular lines by using a protractor is discussed here. To construct a perpendicular to a given line l at a given point A on it, we need to follow the given procedure

3. ### Construction of a Circle | Working Rules | Step-by-step Explanation |

Aug 13, 24 01:27 AM

Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

4. ### Practical Geometry | Ruler | Set-Squares | Protractor |Compass|Divider

Aug 12, 24 03:20 PM

In practical geometry, we study geometrical constructions. The word 'construction' in geometry is used for drawing a correct and accurate figure from the given measurements. In this chapter, we shall…