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 = 1/2 AC. Reason (R): If a tranversal makes equal intercepts on three parallel lines, then another transversal will also make equal intercepts. 1. Assertion (A) is true, Reason (R) is false. 2. Assertion (A) is false, Reason (R) is true. 3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A). 4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Related Questions
Assertion (A): For a Δ ABC, line segment EF is drawn such that E is the midpoint of AB and F is a midpoint of AC. Then the quadrilateral formed EFCB is a trapezium.
Reason (R): The line segment joining the midpoint of two sides of a triangle is parallel to the third side.
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 a Δ DEF, we have DE = EF = DF = 6 cm. A line segment PQ is drawn parallel to DF such that EP = 3 cm. Then we can conclude that PQ = 3 cm.
Reason (R): Any line segment drawn inside a triangle parallel to the base of the triangle cuts the removing two sides in half.
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).
ABCD is a rhombus with P, Q and R as mid-points of AB, BC and CD respectively. Prove that PQ ⊥ QR.
The diagonals of a quadrilateral ABCD are perpendicular. Show that the quadrilateral formed by joining the mid-points of its adjacent sides is a rectangle.