Advertisements
Advertisements
प्रश्न
Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.
Advertisements
उत्तर

Proof: Diagonals of //gm bisect each other.
MD = MB
Also ∠ADB = ∠DBN (Alternate ∠s)
& ∠DML = ∠BMN (Vert. opp. ∠s)
∆DML = ∆BMN
LM = MN
M is mid-point of LN.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Given a parallelogram ABCD. Complete each statement along with the definition or property used.

- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
Construct ☐ PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ☐ PQRS is a parallelogram, which of the given information is unnecessary?
Construct ☐ BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?
ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.

Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
In parallelogram LOST, SN ⊥ OL and SM ⊥ LT. Find ∠STM, ∠SON and ∠NSM.

In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
