Advertisements
Advertisements
प्रश्न
Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Advertisements
उत्तर
Join AC.
P and Q are mid-points of AB and BC respectively.
∴ PQ || AC, PQ = `(1)/(2)"AC"`.........(i)
S and R are mid-points of AD and DC respectively.
∴ SR || AC, SR = `(1)/(2)"AC"`.........(ii)
From (i) and (ii)
PQ = SR
Therefore, PQRS is a parallelogram.
Since, diagonals of a parallelogram bisect each other
Therefore, PQ and QS bisect each other.
APPEARS IN
संबंधित प्रश्न
In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC =
21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.
In Fig. below, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are
respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°.
ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the
mid-points of the sides, in order, is a rectangle.
Let Abc Be an Isosceles Triangle in Which Ab = Ac. If D, E, F Be the Mid-points of the Sides Bc, Ca and a B Respectively, Show that the Segment Ad and Ef Bisect Each Other at Right Angles.
L and M are the mid-point of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.
In trapezium ABCD, AB is parallel to DC; P and Q are the mid-points of AD and BC respectively. BP produced meets CD produced at point E.
Prove that:
- Point P bisects BE,
- PQ is parallel to AB.
In parallelogram ABCD, E and F are mid-points of the sides AB and CD respectively. The line segments AF and BF meet the line segments ED and EC at points G and H respectively.
Prove that:
(i) Triangles HEB and FHC are congruent;
(ii) GEHF is a parallelogram.
In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find DE, if AB = 8 cm
Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.
The diagonals AC and BD of a quadrilateral ABCD intersect at right angles. Prove that the quadrilateral formed by joining the midpoints of quadrilateral ABCD is a rectangle.
