Q10 of 109 Page 330

The diagonals of a rhombus, ABCD intersect at the point O. If ∠BDC = 50°, then ∠OAB = ?

∠BDC = ∠ABD (Alternate interior angles)

∠ABD = 50^o

Now, In ∆AOB,

∠DBA = 50^o and ∠AOB = 90^o

Thus, ∠OAB = 180^o − (90^o + 50^o)

∠OAB = 180° - 140°

∠OAB = 40^o

∴ Option B is correct.

The diagonals of a rectangle ABCD intersect at the point O. If ∠BOC = 50°, then ∠OAD = ?

Match the following column:

Column I	Column II
(a) Sum of all the angles of a quadrilateral is	(p) Right angles
(b) In a \|\|gm, the angle bisectors of two adjacent angles intersect at	(q) Rectangle
(c) Angle bisectors of a \|\|gm form a	(r) 90^o
(d) The diagonals of a square are equal and bisect each other at an angle of	(s) 4 right angles

The correct answer is:

(a) -……, (b) -……..,

ABCD is a trapezium in which AB || CD and AD = BC, then ∠A = ∠B is

Look at the statements given below:

I. If AD, BE and CF be the altitudes of a ΔABC such that AD = BE = CF, then ΔABC is an equilateral triangle.

II. If D is the mid-point of hypotenuse AC of a right ΔABC, then BD = AC.

III. In an isosceles ΔABC in which AB = AC, the altitude AD bisects BC.

Which is true?

A. I only B. II only

C. I and III D. II and III