Question

Statement (1): AD is median of triangle ABC and DE is parallel to BA. Then DE will bisect AC.

Statement (2): DE is the median of ΔADC.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

By the converse of the midpoint theorem, a line drawn through the midpoint of one side parallel to another side bisects the third side, making E the midpoint of AC. Since E is the midpoint of AC in triangle ADC, the segment DE connects a vertex to the midpoint of the opposite side, which confirms it is a median of ΔADC.