Mathematics
Assertion (A): If two triangles are congruent to each other then the ratio of corresponding side is 1 : 1.
Reason (R): Two triangles are congruent if and only if they have same shape and size.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Triangles
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Answer
The reason states, two triangles are congruent if and only if they have same shape and size.
This statement is the precise definition of congruent triangles. Congruence means that one triangle can be perfectly superimposed on the other, covering it exactly.
∴ Reason (R) is true.
If corresponding sides are equal, for example, if side AB of the first triangle corresponds to side DE of the second triangle, and they are equal in length (AB = DE), then their ratio is = 1. This applies to all pairs of corresponding sides.
Therefore, the ratio of corresponding sides is indeed 1 : 1.
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason (or explanation) for Assertion (A).
Hence, option 3 is the correct option.
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Related Questions
If the lengths of two sides of an isosceles triangle are 4 cm and 10 cm, then the length of the third side is
4 cm
10 cm
7 cm
14 cm
Consider the following two statements :
Statement 1: If two angles and one side of a triangle is equal to two angles and one side of an other triangle then the two triangles are congruent.
Statement 2: The angle opposite to equal sides of an isosceles triangle are equal.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): In the adjoining figure, Δ ABC ≅ Δ PQR.
Reason (R): Two triangles are congruent if two angles and included side of One triangle are equal to two angles and the included side of other triangle.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Assertion (A): Two triangles are congruent to each other by RHS rule of congruency. The base of the one triangle is 6 cm and the height is 4 cm. The sum of area of two triangle is 24 cm2.
Reason (R): Two triangles are congruent if they have same shape and size. Congruent triangles have equal area.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).