Question

Assertion: A median of a triangle divides it into 2 triangles of equal area.

Reason: The two triangles so formed are congruent.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is true but R is false.

Explanation:

• The assertion is True. By definition, a median connects a vertex to the midpoint of the opposite side, thus dividing the original triangle into two smaller triangles that share the same base length and height, which makes their areas equal.
• The reason given is: “The two triangles so formed are congruent.” This is false because the two triangles divided by the median are not necessarily congruent; they only have equal area, not necessarily equal sides or angles. Congruence requires equality of all corresponding sides and angles, which is not guaranteed here.