Ray

Line

Intersecting Lines

Parallel Lines

Line Segment

RAY: A part of a line, with one endpoint, that continues without end in one direction

LINE: A straight path extending in both directions with no endpoints

LINE SEGMENT: A part of a line that includes two points, called endpoints, and all the points between them

INTERSECTING LINE: The two lines in the same plane are not parallel, they will intersect at a common point. Those lines are intersecting lines. Here C is the common point of AE and DB

PARALLEL LINES: Lines that never cross and are always the same distance apart

Perpendicular Lines

Two lines that intersect to form a right angles

Right Angle:An angle that forms a square corner

Acute Angle:An angle less than a right angle

Obtuse Angle:An angle greater than a right angle

Straight Angle: It is equal to 180°

Reflex Angle: An angle which is more than 180° but less than 360°

Complementary Angles: Two angles adding up to 90° are called complementary angles.

Here ABD + DBC are Complementary.

Supplementary Angles: Two angles adding up to 180° are called supplementary.

ABD + DBC are supplementary

Transversal: A Transversal is a line that intersect two parallel lines at different points.

Vertical Angles: Two angles that are opposite angles

1 2

3 4

5 6

7 8

t∠1 ≅ ∠ 4∠2 ≅ ∠ 3∠5 ≅ ∠ 8∠6 ≅ ∠ 7

Linear Pair: Two angles that form a l ine (sum=180°)

1 2

3 4

5 6

7 8

t

∠5+∠6=180∠6+∠8=180∠8+∠7=180∠7+∠5=180

∠1+∠2=180∠2+∠4=180∠4+∠3=180∠3+∠1=180

Corresponding Angles: Two angles that occupy corresponding positions are equal.

∠1 ≅ ∠ 5∠2 ≅ ∠ 6∠3 ≅ ∠ 7∠4 ≅ ∠ 8

t

1 2

3 4

5 6

7 8

Alternate Interior Angles: Two angles that lie between parallel lines on opposite side.

∠3 ≅ ∠ 6∠4 ≅ ∠ 5

1 2

3 4

5 6

7 8

Co-Interior Angles: Two angles that lie between parallel lines on the same side of the transversal

1 2

3 4

5 6

7 8

3 +∠5 = 1804 +∠6 = 180

Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal

1 2

3 4

5 6

7 8

2 ≅ ∠ 71 ≅ ∠ 8

Angle Sum Property Of Triangle: The sum of the angles of a triangle is 180°.

1

23

1 + 2 + 3 = 180°

Property of Exterior Angle: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Angle 1,2,3 are exterior angles of triangle

• Vertically Opposite Angles are equal

To Proof – Vertically Opposite Angles are equal

Solution - ∠b + ∠n = 180° ( LINEAR PAIR)

∠b + ∠m = 180° ( LINEAR PAIR)

EQUATING BOTH THE EQUATIONS

→ ∠b + ∠n = ∠b + ∠m

→ ∠n = ∠m

Hence Proved

• Angle Sum Property Of A Triangle is 180°

To Proof -Angle Sum Property Of a Triangle is 180°

Construction - Draw ↔m parallel to BC

Solution - ∠4 = ∠1 (Alternate Interior Angles)

∠5 = ∠2 (Alternate Interior Angles)

∠3 + ∠4 + ∠5 = 180° ( Angles on the same line are supplementary)

Substituting the values

∠3 + ∠1 + ∠2 = 180° (Angle Sum Property)

Hence Proved

Made by:

Shaik Mallika