Mathematics
Assertion (A): Refer to the adjoining figure. Three lines p, q, r are parallel to each other and PQ = QR = 1 cm. Then we conclude that AB = AC.
Reason (R): If a tranversal makes equal intercepts on three parallel lines, then another transversal will also make equal intercepts.
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).
Mid-point Theorem
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Answer
According to equal intercept theorem, if a tranversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
∴ Reason (R) is true.
Three lines p, q, r are parallel to each other
PQ = QR = 1 cm.
⇒ PQ = QR
By equal intercept theorem.
⇒ AB = BC
From figure, AC = AB + BC
⇒ AC = AB + AB
⇒ AC = 2AB
⇒ AB = AC.
∴ 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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