Mathematics
Statement 1: AD is median of triangle ABC and DE is parallel to BA.
Statement 2: DE is median of triangle ADC.
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.
Mid-point Theorem
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Answer
In △ ABC,
From figure,
BD = DC.
∴ D is the mid-point of BC.
A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.
So, AD is the median of triangle ABC.
So, statement 1 is true.
By converse of mid-point theorem,
The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side.
Since, D is mid-point of BC and AB || DE
∴ E is the mid-point of AC.
Thus, DE is a median of triangle ADC.
So, statement 2 is true.
∴ Both the statements are true.
Hence, option 1 is the correct option.
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