91Ó°ÊÓ

Here, both the quadrilaterals are congruent and$\stackrel{¯}{OR}$ is the common side of the two congruent quadrilaterals.

If two quadrilaterals are congruent then the following conditions are satisfied:

1. Corresponding sides of the two quadrilaterals are congruent.

2. Corresponding angles of the two quadrilaterals are congruent.

As quadrilateral $NORE$is congruent to quadrilateral $MORA$,

$\stackrel{¯}{NO}â‰\dots \stackrel{¯}{MO}$(Corresponding sides of congruent quadrilaterals are congruent).

As the midpoint of the line segment is a point that divides it into two congruent segments, $O$is the midpoint of $\stackrel{¯}{NM}$.

Therefore, $O$ is the midpoint of$\stackrel{¯}{NM}$ is true.

Here, both the quadrilaterals are congruent and $\stackrel{¯}{OR}$is the common side of the two congruent quadrilaterals.

If two quadrilaterals are congruent then the following conditions are satisfied:

1. Corresponding sides of the two quadrilaterals are congruent.

2. Corresponding angles of the two quadrilaterals are congruent.

As quadrilateral $NORE$is congruent to quadrilateral $MORA$,

$∠NORâ‰\dots ∠MOR$(Corresponding angles of congruent quadrilaterals are congruent).

Therefore, $∠NORâ‰\dots ∠MOR$is true.

Here, both the quadrilaterals are congruent and $\stackrel{¯}{OR}$is the common side of the two congruent quadrilaterals.

From part (b),

$∠NORâ‰\dots ∠MOR$

So,

$m∠NOR=m∠MOR$(Congruent angles are equal to each other).

$m∠NOR+m∠MOR={180}^{∘}$( $∠NOR,∠MOR$form a linear pair and measure of linear pair of angles is ${180}^{∘}$).

So,

$m∠NOR+m∠MOR={180}^{∘}$

Since $∠NOR=∠MOR$, then,

$\begin{array}{c}2∠NOR={180}^{∘}\\ ∠NOR={90}^{∘}\end{array}$

So,

$\stackrel{¯}{RO}âŠ\yen \stackrel{¯}{NM}$ (Two lines segments are perpendicular if they form a right angle).

Therefore, $\stackrel{¯}{RO}âŠ\yen \stackrel{¯}{NM}$is true.