Mathematics
ABCD is a rhombus with P, Q and R as mid-points of AB, BC and CD respectively. Prove that PQ ⊥ QR.
Related Questions
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).
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.
If D, E and F are mid-points of the sides BC, CA and AB respectively of a △ABC, prove that AD and FE bisect each other.