Problem
GEO-B1-M02-P010 Two Points on the Sides of an Angle
#10
★★☆☆☆ Level 2 of 5
On the sides of angle \(A\), points \(B,M\) lie on one side and \(C,N\) on the other, with \(AB=AC\) and \(AM=AN\). Prove that \(BN=CM\).
Compare triangles \(ABN\) and \(ACM\).
In triangles \(ABN\) and \(ACM\), we have \(AB=AC\), \(AN=AM\), and the included angle in both triangles is angle \(A\). By SAS, the triangles are congruent. Therefore the corresponding sides \(BN\) and \(CM\) are equal.
Good practice in choosing a “crossed” pair of triangles.