## Pre-Requisires

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We recall that

(i) A line-segment has two end points.

(ii) A ray has only one end point (its vertex);and

(III) A line has no end points on either side.

An angle is formed when two lines (or rays or line-segments) meet.

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**Important Formulas | Lines and Angles**

When two lines l and m meet, we say they intersect; the meeting point is calledthe point of intersection.

When lines drawnon a sheet of paper do not meet, howeverfar produced, we call them to be *parallel *lines.

**Point**: A point name a location.

**Line**: A line is perfectlystraight and extends forever in both direction.

**Line segment**: A line segmentis the part of a line betweentwo points.

**Ray**: A ray is part of a line that starts at one point and extendsforever in one direction.

**Intersecting lines**: Two or more lines that have one and only one point in common.

The common point where all the intersecting lines meet is called the point of

intersection.

**Transversal**: A line intersects two or more lines that lie in the same plane in distinct points.

**Parallel lines**: Two lineson a plane that nevermeet. They distance apart.

**Complementary Angles**: Two angles whose measures add to 90^O **Supplementary Angles**: Two angles whose measures add to 180 ^o

**Adjacent Angles**: Two angles have a common vertex and a

common interiorpoints.

**Linear pairs**: A pair of adjacentangles whose non-common sides are oppositerays. **Vertically Opposite Angles**: Two angles formed by two intersecting lines have common arm.

**Angles made by Transversal**: When two lines are intersecting by a transversal, eight anglesare formed.

**Transversal of Parallel Lines**: If two parallel lines are intersected by a transversal, each pair of:

Corresponding angles are congruent. Alternateinterior angles are congruent. Alternateexterior angles are congruent.

If the transversal is perpendicular to the parallellines, all of the angles formed are congruent to 90 o angles.

1. A linewhich intersects two or more given lines at distinct points is called a transversal to the given lines.

2. Lines in a plane areparallel if theydo not intersect when produced indefinitely in either direction.

3. The distance between two intersecting lines is zero.

4. The distance between two parallel lines is thesame everywhere andis equal tothe perpendicular distance between them.

5. If two parallel lines are intersected by a transversal then (i) pairs ofalternate (interior orexterior) angles are equal. (ii) pairs of corresponding angles are equal. (iii) interior angles onthe same sideof the transversal are supplementary. 6. If twonon-parallel lines areintersected by transversal then none of (i), (ii) and (iii) hold true in 5. 7. If twolines are intersected by a transversal, thenthey are parallel ifany one of thefollowing is true: (i) The angles of a pair of corresponding angles are equal. (ii) The angles of a pairof alternate interior angles are equal. (iii) The angles of a pairof interior angles on the sameside of the transversal are supplementary.

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