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 midpoints 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

ANSWER:
(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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Similar questions

Q. For an isosceles right-angled triangle having each of equal sides 'a', we have
I.

Area = \frac{1}{2} a^{2}

II.

Perimeter = (2 + \sqrt{2}) a

III. Hypotenuse = 2a
Which of the following is true?
(a) I only
(b) II only
(c) I and II
(d) I and III

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)

State true or false:

The bisectors of any two adjacent angles of a square form an isosceles-right-angled triangle.

In an isosceles triangle $A B C$ , with $A B = A C$ ,the bisectors of $∠ B$ and $∠ C$ interest each other at $O$ .join $A$ to $O$ show that:
(i) $O B = O C$
(ii) $A O$ bisects $∠ A$

In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:

(i) OB = OC (ii) AO bisects ∠A

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ANSWER: (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.

ANSWER:
(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.