Mathematics
In triangle ABC, AD is the median and DE, drawn parallel to side BA, meets AC at point E. Show that BE is also a median.
Mid-point Theorem
5 Likes
Answer
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.
In △ ABC,
AD is the median.
∴ D is the mid-point of BC.
Since, DE || AB
∴ E is the mid-point of AC (By converse of mid-point theorem)
Join BE.
∴ BE is also the median of triangle ABC.
Hence, proved that BE is also the median of triangle ABC.
Answered By
3 Likes
Related Questions
In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that :
(i) BP = 2AD
(ii) O is mid-point of AP.
In a trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.
Prove that :
AB + DC = 2EF.
In △ ABC, AD is the median and DE is parallel to BA, where E is a point in AC. Prove that BE is also a median.
Adjacent sides of a parallelogram are equal and one of diagonals is equal to any one of the sides of this parallelogram. Show that its diagonals are in the ratio .