Mathematics
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.
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,
Since, AD is the median.
∴ D is the mid-point of BC.
Since, D is mid-point of BC and DE || AB.
∴ E is the mid-point of AC. (By converse of mid-point theorem)
Join BE.
Hence, proved that BE is also a median.
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.
A school designing a triangular garden △ABC. To construct a walking path inside the garden, the gardener marks the mid-points of two sides: point D is the mid-point of side AB and point E is the midpoint of side AC. The path DE is drawn to connect these mid-points. The length of side BC of the triangular garden is 12 m, AB = 10 m and AC = 10 m.
Based on the above information answer the following:
(i) What is the length of path DE?
(ii) Assign a special name to Quadrilateral BCED and find its perimeter.