Study the statements carefully. (P) The line segment joining a vertex of a triangle to the mid point of its opposite side is called a median of the triangle. A triangle has 3 medians. (Q) The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle. A triangle has 3 altitudes. Which of the following options hold? A. Both (P) and (Q) are true. B. Both (P) and (Q) are false. C. (P) is true, (Q) is false. D. (P) is false, (Q) is true.
Median: A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
Altitude: An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). Every triangle has exactly three altitudes, one from each vertex, and they all intersect each other at the triangle's orthocentre.
From the above definitions, we can conclude that both the statements (P) and (Q) are correct.
A. Both (P) and (Q) are true is the correct option.
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