A rectangular MORE, is shown below:

Answer the following questions by giving appropriate reason.

(i) Is RE = OM? (ii) Is MYO = RXE?

(iii) Is MOY = REX? (iv) Is ∆MYO = ∆RXE?

(v) Is MY = RX?

(i) Yes,

∵ MORE is a rectangle.

And, the opposite sides of the rectangle are equal.

∴ RE = OM

(ii) Yes,

In the MORE rectangle,

MY and RX are perpendicular to OE

⇒ ∠RXO = ∠RXE = ∠MYE = ∠MYO = 90⁰

∴ ∠MYO = ∠RXE

(iii) Yes,

∵ in rectangle MORE, RE||OM and EO is transveral.

From the property of alternate interior angles being equal.

∴ ∠MOE = ∠OER

⇒ ∠MOY = ∠REX

(iv) Yes,

In, ΔMYO and Δ RXE,

MO = RE

∠MOY = ∠REX

∠MYO = ∠RXE

∴ ΔMYO ≅ ΔRXE

(v) Yes.

Corresponding parts of congruent triangles are equal.