Question

State the property that is used in each of the following statements $?$
If $a\parallel b,$ then $\angle 1=\angle 5$
If $\angle 4=\angle 6,$ then $a\parallel b$
If $\angle 4+\angle 5={180}^{\circ },$ then $a\parallel b$

Answer 1

$1.$ If $a||b$ then $\angle 1=\angle 5$

(corresponding angles)

$2.$ $\angle 4=\angle 6$

$\angle 4=\angle 7$ (corresponding angles)

$\angle 4=\angle 6$ (alternative angle)

$3.$ $\angle 4+\angle 5={180}^o$

$\angle 4=\angle 7$

$\angle 4=180-\angle 5$

$\Rightarrow \angle 5+\angle 4={180}^o$.