
Two lines n and p intersect at a point.
Proof:
Let us consider lines n and p are not intersecting, and
then it means they are parallel to each other i.e.,
… (i)
Since, lines n and p are perpendicular to l and m
respectively, but from equation (i)
, it is implied
that
, it is a contradiction.
Thus, our assumption is wrong.
Hence, lines n and p intersect at a point.
Question: 6
Prove that a triangle must have at least two acute
angles.
Solution:
Given:
is a triangle
To prove:
must have two acute angles.
Proof:
Let us consider the following cases:
Case I:
When two angles are
:
Suppose two angles are
and
.