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Question
A rectangular MORE is shown below:
Answer the following questions by giving appropriate reason.
- Is RE = OM?
- Is ∠MYO = ∠RXE?
- Is ∠MOY = ∠REX?
- Is ΔMYO ≅ ΔRXE?
- Is MY = RX?
Solution
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.
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