Advertisements
Advertisements
Question
The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2. Can it be a parallelogram? Why or why not?
Advertisements
Solution
No, it cannot be a parallelogram because the diagonal of a parallelogram are always bisect each other i.e. in the ratio 1:1.
APPEARS IN
RELATED QUESTIONS
Diagonals of a parallelogram `square`WXYZ intersect each other at point O. If ∠XYZ = 135° then what is the measure of ∠XWZ and ∠YZW?
If l(OY)= 5 cm then l(WY)= ?
The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to ______.
Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.
E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.
Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP = CQ (Figure). Show that AC and PQ bisect each other.
A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.
In the following figure, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.
ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.
P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA = AR and CQ = QR.
Two sticks each of length 5 cm are crossing each other such that they bisect each other. What shape is formed by joining their endpoints? Give reason.
