Materials- Metals &Non-metals Basic Geometry Terms

A point is an exact loca�on inspace or a flat surface Intersec�ng lines are lines that

pass through the same point

Perpendicular lines are linesthat intersect at right angles

Parallel lines are lines thatnever intersect

A line is a collec�on of points thatcon�nues forever in oth direc�ons

A line segment is a part of a linewith two end points

A ray starts from one point andextends in one direc�on forever

An angle is formed when two raysshare an endpoint

points which lie on the same line are collinear points

points which don’t lie on the same line are non - collinear points

PQ

R

A

B

C

Type of Angle

Acute Angle An angle that is less than 90o

An angle that is exactly 90oRight Angle

An angle that is greater than 90o less than 180oObtuse Angle

An angle that is exactly 180oStraight Angle

An angle that is greater than 180o less than 180oReflex Angle

An angle that is exactly 360oFull Angle

Angles that add up to 90oComplementaryAngles

Angles that add up to 180oSupplementaryAngles

AdjacentAngles

Descrip�on Example

46o

90o

130o

308o

360o

180o

38o

52o

180o

Angles with a common side and a commonvertex. 1 and 2 are adjacent angles

Adjacent angles that form a straight line.1 and 2 are adjacent angles

Linear Pair ofAngles

Angles that have a common vertex andwhose arms are formed by the same lines.ver�cally opposite angles are equal.

Ver�callyOpposite Angles

1 + 2 = 180o

1 = 2 and 3 = 4

21

21

23

41

Lines and Angles - Part I

Materials- Metals &Non-metals Transversal

Checking for Parallel Lines

Exterior Angle Property of a Triangle

More about Parallel lines

Angle Sum Property of a Triangle

It is a line that passes through two lines lying in the same plane at two dis�nct points.

If a transversal intersects two lines such that, either any one pair of corresponding angles is equal, or any one pair of alternate interior angles is equal, or any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.

Lines which are parallel to a given line are parallel to each other. I.e., if l�m and m�n then l�n

If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interioropposite angles. I.e.,

If a transversal p intersects two parallel lines l and m , then following angles will be formed.

Interior Angles on the same side of traversal(Co - interior Angles)

Angles Formed by a transversal

Interior

Exterior

p1

5

7 8

6

2

34

l

m

Traversal

p1

5

7 8

6

2

34

l

m

Corresponding Angles

1

7 8

2l

m

Alternate Exterior Angles

1

7 8

2

5 6

34

l

m

p

Alternate Interior Angles

p

5 6

34

l

m

1 = 5 ; 2 = 6 ;3 = 7 ; 4 = 8 ;

1 = 82 = 7

3 = 6 ; 4 = 5 ;

Interior Angles Exterior Angles

5 6

34

l

m

p

l

m

n

3 + 5 = 180o 4 + 6 = 180o

P

Q R

1

2 3

P

Q R S

1

2 34

Sum of all the angles in a triangle is 180o . i.e., 1 + 2 + 3 = 180o

4 = 1 + 2

123

Lines and Angles - Part II