Three statements are given below:
I. In a || gm, the angle bisectors of two adjacent angles enclose a right angle.
II. The angle bisectors of a || gm form a rectangle.
III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.
Which is true?
(a) I only
(b) II only
(c) I and II
(d) II and III

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Solution

(c) I and II

Statements I and II are true. Statement III is false, as the triangle formed by joining the midpoints of the sides of an isosceles triangle is an isosceles triangle.

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Question 5

In an isosceles triangle, one angle is $70^{\circ}$ . The other two angles are of

i) $55^{\circ}$ and $55^{\circ}$
ii) $70^{\circ}$ and $40^{\circ}$
iii) Any measure

In the given option(s) which of the above statement(s) are true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

Fill in the blanks to make the following statements correct :

(i) The triangle formed by joining the mid-points of the sides of an isosceles triangle is ...

(ii) The triangle formed by joining the mid-points of the sides of a right triangle is ....

(iii) The figure formed by joining the mid-points of consecutive sides of a quadrilateral is ....

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