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In Δ 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. - Mathematics

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प्रश्न

In Δ 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.

योग
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उत्तर

Since AD is the median of ΔABC, then BD = DC.

Given, DE || AB and DE are drawn from the midpoint of BC i.e. D, then

by the converse of mid-point theorem,

it bisects the third side which in this case is AC at E.

Therefore, E is the mid point of AC.

Hence, BE is the median of ΔABC.

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Mid-point and Its Converse [ Including Intercept Theorem] - Exercise 12 (B) [पृष्ठ १५४]

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सेलिना Concise Mathematics [English] Class 9 ICSE
अध्याय 12 Mid-point and Its Converse [ Including Intercept Theorem]
Exercise 12 (B) | Q 14 | पृष्ठ १५४

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