Problem
GEO-B1-M02-P008 The Median Is an Altitude
#8
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(M\) is the midpoint of \(BC\), and \(AM\perp BC\). Prove that \(AB=AC\).
Triangles \(ABM\) and \(ACM\) are right triangles with two equal legs.
In triangles \(ABM\) and \(ACM\), we have \(BM=CM\), common side \(AM\), and right angles \(AMB\) and \(AMC\). By SAS, the triangles are congruent. Therefore \(AB=AC\).
A short problem on the converse property of an isosceles triangle.