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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?

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

Solution:

Given, MORE is a rectangle.

(i) In a rectangle the opposite sides are equal.

RE = OM and RO = EM

So, RE = OM

(ii) From the figure,

MY and RX are perpendicular to OE.

So, ∠RXO = 90° and ∠MYE = 90°

Similarly, ∠RXE = 90° and ∠MYO = 90°

Therefore, ∠MYO = ∠RXE

(iii) Since RE || OM with EO as a transversal, the alternate interior angles are equal.

So, ∠MOE = ∠OER

Therefore, ∠MOY = ∠REX

(iv) considering triangles MYO and RXE,

MO = RE

∠MOY = ∠REX

∠MYO = ∠RXE

AAS criterion states that when two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

By AAS criterion, the triangles MYO and RXE are congruent.

Therefore, ∆MYO ≅ ∆RXE

(v) CPCT stands for Corresponding parts of congruent triangles, when two triangles are congruent then their corresponding parts are equal.

By CPCT,

MY = RX

✦ Try This: A parallelogram 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

A parallelogram 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

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 152