Question

Match the following reasons with the given statements of proof

Answer 1

Answer:

Given :  $\overrightarrow{ST} \perp \overrightarrow{SR}$

Or we can say that A ray ST is perpendicular to Ray SR.

By the definition of Perpendicular lines: A  perpendicular lines are lines that intersect at a right angle.

⇒ $\angle RST$ is right angle.

Then, by the definition of the right angle states that the angle bounded by the  two perpendicular lines i.e, an angle of $90^{\circ}$.

⇒ $\angle RST$$= 90^{\circ}$

Addition Angle theorems states that the sum of measure of two angle of an interior angle.

then, by the definition of the addition angle theorem we have ;

$m\angle 1 +m\angle 2 = m\angle RST$         ......[1]

Now, by substituting the value of $\angle RST = 90^{\circ}$ in above equation[1];

$m\angle 1 +m\angle 2 =90^{\circ}$                ......[2]

Subtraction property of Equality states that subtract the same number from both sides of an equation.

Now, subtract $m\angle 2$ from both sides of an equation [2];

$m\angle 1 +m\angle 2 -m\angle 2 =90^{\circ}-m\angle 2$

On simplify we get,

$m\angle 1 =90^{\circ} - m\angle 2$                    Hence proved!

The figure as you can see in the attachment.