Question
A rectangular $\text{MORE}$ is shown below:

Answer the following questions by giving appropriate reason.
$i. \text{Is}\ \text{RE}=\text{OM}$
$ii. \text{Is}\ \angle\text{MYO}=\angle\text{RXE}?$
$iii. \text{Is}\ \angle\text{MOY}=\angle\text{RXE}?$
$iv. \text{Is}\ \triangle\text{MYO}\cong\triangle\text{RXE}?$
$v. \text{Is}\ \angle\text{MY}=\angle\text{RX}?$

Answer

$i.$ Yes, $\text{RE = OM}$
Given, $\text{MORE}$ is a rectangle. Therefore, opposite sides are equal.
$ii.$ Yes $\angle\text{MYO}=\text{RXE}$
here, $\text{MY}$ and $\text{RX}$ are perpendicular to $OE$.
Since, $\angle\text{RXO}=90^\circ\angle\text{RXE}=90^\circ\ \text{and}\ \angle\text{MYO}=90^\circ$
$iii.$ Yes, $\angle\text{MOY}=\angle\text{REX}$
$\ce{RE\|OM}$ and $\text{EO}$ is a transversal
$\angle\text{MOE}=\angle\text{OER}$
$iv. \angle\text{MOY}=\angle\text{REX}$
Yes, $\triangle\text{MOY}\cong\triangle\text{RXE}$
In $\triangle\text{MYO}\ \text{and}\ \triangle\text{RXE}$
$\text{MO = RE}$
$\angle\text{MOY}=\angle\text{REX}$
$\angle\text{MYO}=\angle\text{RXE}$
$\therefore\triangle\text{MOY}\cong\triangle\text{RXE}$
$v.$ Yes, $\text{MY = RX}$
since, these are corresponding parts of congruent triangles.

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