Mathematics
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.
Triangles
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Answer
Given, according to 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.
The above statement is true and the triangles are congruent by two axioms A.A.S. or A.S.A. axiom.
∴ Statement 1 is true.
In an isosceles triangle, the angles opposite to equal sides are equal.
∴ Statement 2 is true.
∴ Both statements are true.
Hence, option 1 is the correct option.
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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).
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).