Mathematics
ABCD is a rhombus with P, Q and R as mid-points of AB, BC and CD respectively. Prove that PQ ⊥ QR.
Mid-point Theorem
26 Likes
Answer
Join AC and BD.
Diagonals of rhombus intersect at right angle.
∠MON = 90°
In △BCD,
Q and R are mid-points of BC and CD.
RQ || DB and RQ = DB
RQ || DB ⇒ MQ || ON
From figure,
∠MON + ∠MQN = 180° (Sum of alternate angles of quadrilateral = 180°)
∠MQN = 180° - 90° = 90°
∴ PQ ⊥ QR.
Hence, proved that PQ ⊥ QR.
Answered By
17 Likes
Related Questions
In the adjoining figure, ABCD is a parallelogram and E is mid-point of AD. DL || EB meets AB produced at F. Prove that B is mid-point of AF and EB = LF.
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.
In △ABC, D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 8 cm and BC = 9 cm, find the perimeter of the parallelogram BDEF.
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.