Question

A rectangular MORE is shown below:

Answer the following questions by giving appropriate reason.

1. Is RE = OM?
2. Is ∠MYO = ∠RXE?
3. Is ∠MOY = ∠REX?
4. Is ΔMYO ≅ ΔRXE?
5. Is MY = RX?

Answer 1

i. Yes, RE = OM

Given, MORE is a rectangle.

Therefore, opposite sides are equal.

ii. Yes, ∠MYO = ∠RXE

Here, MY and RX are perpendicular to OE.

Since, ∠RXO = 90°

⇒ ∠RXE = 90° and ∠MYE = 90°

⇒ ∠MYO = 90°

iii. Yes, ∠MOY = ∠REX

∵ RE || OM and EO is a transversal.

∴ ∠MOE = ∠OER   ...[∵ Alternative interior angles]

⇒ ∠MOY = ∠REX

iv. Yes, ∆MYO ≅ ∆RXE

In ∆MYO and ∆RXE

MO = RE   ...[Proved in (i)]

∠MOY = ∠REX   ...[Proved in (iii)]

∠MYO = ∠RXE   ...[Proved in (ii)]

∴ ∆MYO = ∆RXE  ...[By AAS]

v. Yes, MY = RX

Since, these are corresponding parts of congruent triangles.