Lines and Angles | Study

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

Point of intersection: Point of intersection is a common point at which the intersecting lines meet.

Transversal: Transversal is a line that intersects two or more lines which lie in the same plane at distinct points.

Parallel lines: Parallel lines are the lines on a plane which never meet. They are at a distance apart.

Complementary Angles: Complementary angles are the angles whose total is equal to 90^o .

Supplementary Angles: Suplementary angles are the angles whose total is equal to 180^o

Adjacent Angles: Adjacent Angles are the angles which have a common vertex and a common interior points.

Linear Pair of Angles: Linear pair of angles is a pair of adjacent angles whose non-common sides are opposite rays.

Vertically Opposite Angles: Vertically opposite angles are the angles formed by two intersecting lines which have the have common arms.

Angles made by Transversal:

When two lines are intersecting by a transversal, eight angles are 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.
• Alternate exterior angles are congruent.

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

1. A line which intersects two or more given lines at distinct points is called a transversal to the given lines.
2. Lines in a plane are parallel if they do 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 the same everywhere and is equal to the perpendicular distance between them.

If two parallel lines are intersected by a transversal then:

• pairs of alternate (interior orexterior) angles are equal.
• pairs of corresponding angles are equal.
• interior angles onthe same sideof the transversal are supplementary.

6. If two non-parallel lines are intersected by transversal then none of (i), (ii) and (iii) hold true in 5. 7.

If two lines are intersected by a transversal, then they are parallel if any one of the following is true:

• The angles of a pair of corresponding angles are equal.
• The angles of a pairof alternate interior angles are equal.
• The angles of a pairof interior angles on the sameside of the transversal are supplementary.