Mathematics
D and E are mid-points of the sides AB and AC of △ABC and O is any point on the side BC. O is joined to A. If P and Q are mid-points of OB and OC respectively, then DEQP is
a square
a rectangle
a rhombus
a parallelogram
Answer
In △ABC,
D and E are respective midpoints of AB and AC.
∴ DE || (BC or PQ) ……(1)
Again in △ABO,
D and P are respective midpoints of AB and BO.
∴ DP || AO ……..(2)
In △ACO,
E and Q are respective midpoints of AC and CO.
∴ EQ || AO ……..(3)
From 2 and 3 we get,
DP || EQ …….(4)
From 1 and 4 we get,
DE || PQ and DP || EQ
∴ DEQP is a parallelogram.
Hence, Option 4 is the correct option.
Related Questions
In a △ABC, AB = 3 cm, BC = 4 cm and CA = 5 cm. If D and E are mid-points of AB and BC respectively, then the length of DE is
1.5 cm
2 cm
2.5 cm
3.5 cm
In the adjoining figure, ABCD is a rectangle in which AB = 6 cm and AD = 8 cm. If P and Q are mid-points of the sides BC and CD respectively, then the length of PQ is
7 cm
5 cm
4 cm
3 cm
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if
PQRS is a parallelogram
PQRS is a rectangle
the diagonals of PQRS are perpendicular to each other
the diagonals of PQRS are equal.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order is a rhombus if
ABCD is a parallelogram
ABCD is a rhombus
the diagonals of ABCD are equal
the diagonals of ABCD are perpendicular to each other.