Geometry - Lines

Geometry is basically the study of different properties of point, line and plane.

Angle
Right angle: An angle of 90° is called a right angle.
Acute angle: An angle of less than 90° is called an acute angle.
Obtuse angle: An angle of greater than 90° is called an obtuse angle.
Reflex angle: An angle of greater than 180° is called reflex angle.
Complementary angles: If the sum of the two angles is 90°, then they are called complementary angles.
Supplementary angles:  If the sum of the two angles is 180°, then they are called supplementary angles.

Angle Relations: 

Vertically opposite angles: If two lines intersect each other, then the vertically opposite angles are equal.
∠$\mathrm{\angle }$a = ∠$\mathrm{\angle }$c and ∠$\mathrm{\angle }$b = ∠$\mathrm{\angle }$d
a, c and b, d are vertically opposite angles.

Angles in parallel lines: If a transversal intersects two parallel lines:

a. each pair of consecutive interior angles are supplementary.
∠$\mathrm{\angle }$4 + ∠$\mathrm{\angle }$5 = 180°
∠$\mathrm{\angle }$3 + ∠$\mathrm{\angle }$6 = 180°

b. each pair of alternate interior angles are equal.
∠$\mathrm{\angle }$5 =∠$\mathrm{\angle }$3, ∠$\mathrm{\angle }$6 = ∠$\mathrm{\angle }$4
∠$\mathrm{\angle }$5 = ∠$\mathrm{\angle }$3 =∠$\mathrm{\angle }$1 =∠$\mathrm{\angle }$7
∠$\mathrm{\angle }$6 = ∠$\mathrm{\angle }$4 = ∠$\mathrm{\angle }$2 = ∠$\mathrm{\angle }$8

Collinear: Three or more than three points are said to be collinear, if there is a line which contains them
all.
Concurrent: Three or more than three lines are said to be concurrent, if there is a point which lies on them
all.

Proportionality Theorem:

In the above diagram, ABBC=DEEF${\displaystyle \frac{AB}{BC}=\frac{DE}{EF}}$ or ACBC=DFEF${\displaystyle \frac{AC}{BC}=\frac{DF}{EF}}$