Advertisements
Advertisements
प्रश्न
ABCD is a parallelogram, M is the mid-point of BD and BM bisects ∠B. Then ∠AMB =
पर्याय
45°
60°
90°
75°
Advertisements
उत्तर
Figure is given as follows:
ABCD is a parallelogram.
It is given that :
BM bisects ∠B
Therefore,
∠1 = ∠2
But,
∠2 = ∠3 (Alternate interior opposite angles asDC || AB )
Therefore,
∠1 = ∠3
In ΔABD,
∠1 =∠3
Sides opposite to equal angles are equal.
Thus,
AD = AB
Also,
CD = AB (Opposite sides of a parallelogram are equal)
Thus,
CD = AD
ABCD is a parallelogram with AD = AB
Therefore,
ABCD is a rhombus.
And we know that diagonals of the rhombus bisect each other at right angle.
Thus, ∠AMB = 90°
Hence the correct choice is (c).
APPEARS IN
संबंधित प्रश्न
The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that
(i) Quadrilateral ABED is a parallelogram
(ii) Quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) Quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ΔABC ≅ ΔDEF.
The following statement are true and false .
If all the angles of a quadrilateral are equal, it is a parallelogram .
The following statement are true and false .
If three angles of a quadrilateral are equal, it is a parallelogram .
If ABCD is a rhombus with ∠ABC = 56°, find the measure of ∠ACD.
Complete the following statement by means of one of those given in brackets against each:
Consecutive angles of a parallelogram are ...................
The figure formed by joining the mid-points of the adjacent sides of a rectangle is a
If one angle of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is
The diagonals of a parallelogram ABCD intersect at O. If ∠BOC = 90° and ∠BDC = 50°, then ∠OAB =
