Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): If any two sides of a right trangle are equal to the corresponding sides an another right triangle then the triangles are congruent.
Reason (R): Two triangles are congruent if the three sides of one triangle are equal to thit three corresponding sides of the other triangle.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(d): For two right triangles to be congruent, hypotenuse and one side of one triangle must be equal to the hypotenuse and the corresponding side of the other.
$\therefore A$ is false.
$R$ is true (by the definition of SSS congruence).

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MCQ 21 Mark

Assertion (A): Two triangles are congruent if two sides and any one angle of one are respectively equal to two sides and the corresponding angle of the other.
Reason (R): SAS congruence is one of the conditions for congruence of two triangles.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(d): A is false, since two triangles are congruent if two sides and included angle of one are equal to two sides and included angle of the other.
$R$ is true, as SAS congruence is one of the conditions for congruence of two triangles.

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MCQ 31 Mark

Assertion (A): If two squares have equal areas, they are congruent.
Reason (R): If two rectangles have equal areas, they are congruent.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
✓
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: C.

Assertion (A) is true but Reason (R) is false.

(c): Area of a square with sides of length ' $a$ ' is $a^2$.
So, if two squares have equal areas then they have equal side length and therefore they are congruent.
$\therefore A$ is true.
Consider two rectangles one having $l=10 cm, b=2 cm$ and the other having $l=5 cm$, $b=4 cm$.
Both rectangles have the same area of $20 cm^2$ but they are not congruent since they do not have the same length and breadth. $\therefore R$ is false.

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MCQ 41 Mark

Assertion (A): Two circles having the same circumference are always congruent.
Reason (R): Congruent triangles have equal areas.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: B.

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

(b): Circumference of a circle with radius $r$ is $C=2 \pi r$.
So, if two circles have the same circumference then they have the same radius and therefore they are congruent.
$\therefore A$ is true.
Congruent triangles always have equal areas.
$\therefore R$ is also true but R is not the correct explanation of A .

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MATHS Assertion (A) & Reason (B) MCQ

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