Chapter 2.8, Problem 8PSA

To determine

Two given angles are congruent

Answer to Problem 8PSA

  $\angle 5\text{ \& }\angle 6$ are congruent

Explanation of Solution

Given information :

Two given angles $\left(\angle 4\&\angle 6\right)$ are congruent

Two parallel lines are crossed by a transversal as per the given figure

Formula used:

Vertically opposite angles are always equal

Congruency means same size and same shape

Corresponding angles formed are equal, when a transversal cuts two parallel lines

Proof:

  $\begin{array}{l}\angle 4\cong \angle 6\mathrm{.......}(\text{given)}\\ \therefore \angle 4=\angle 6\mathrm{.......}(\text{i})\text{ [same size and shape by definition of congruency]}\end{array}$

And,

  $\angle 4=\angle 5\mathrm{.......}\text{ (ii) [vertically opposite angles]}$

From (i) and (ii), we have

  $\angle 5=\angle 6\mathrm{..........}\text{ [these are corresponding angles]}$

Hence Proved