Three Statements are given below: I.In a, Parallelogram the angle… - Vidyadip

MCQ

Three Statements are given below:
$I$.In a, Parallelogram the angle bisectors of $2$ adjacent angles enclose a right angle.
$II$.The angle bisector of a Parallelogram 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 of the statement/ statements is/ are True?

A
$II$
B
$I$
C
$I$ and $III$
✓
$I$ and $II$

✓

Answer

Correct option: D.

$I$ and $II$

$I.$The adjacent angles of a parallelogram are supplementary.
Their halves add up to $90^\circ $.
So the angle bisectors enclose a right angle.
$II$.All the adjacent angle bisectors enclose right angles.
So we have a rectangle being enclosed by the angle bisectors of a parallelogram.
$III$.The triangle formed by joining the mid$-$points of the sides of an isosceles triangle is always an isosceles triangle, because halves of equal sides are also equal.

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