Problem
GEO-B1-M02-P004 Median to the Base
#4
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), \(AB=AC\). Point \(M\) is the midpoint of \(BC\). Prove that \(\triangle ABM\) and \(\triangle ACM\) are congruent.
Use \(AB=AC\), \(BM=CM\), and common side \(AM\).
We have \(AB=AC\) by the condition, \(BM=CM\) because \(M\) is the midpoint of \(BC\), and \(AM\) is common. Hence \(\triangle ABM=\triangle ACM\) by SSS.
You can immediately ask which properties of the median follow.