Question

Explain the different properties of lines and angles.

Answer 1

I. Lines and Angles

Given two parallel lines, 1) Corresponding angles $=\angle 1$ and $\angle 3$ are equal.

$\angle 2$ and $\angle 4$

$\angle 6$ and $\angle 8$

$\angle 5$ and $\angle 7$

i.e. $\angle 1=\angle 3.\angle 2=\angle 4$ and so on.

II) Alternate interior $\angle 8=\angle 6$ and $\angle 4$ are equal.

$\angle 5$ and $\angle 3$

i.e. $\angle 6=\angle 4$ and $\angle 5=\angle 3$

3) Alternate angles on same side of the transversal sum upto 180^\circ

i.e. $\angle 5+\angle 4={180}^{\circ }$

$\angle 6+\angle 3={180}^{\circ }$

4) Vertically opposite $\angle$ s are also equal

i.e. $\angle 2=\angle 6,\angle 1=\angle 5$ and so on

II Sum of angles of a triangle is ${180}^{\circ }$

$\angle 1+\angle 2+\angle 3={180}^{\circ }$

III Exterior angle property $\to [\angle 4=\angle 1+\angle 2]$