Problem
GEO-B1-M07-P012 Find Congruent Triangles After a Construction
#12
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(M\) is the midpoint of \(BC\). Extend \(AM\) beyond \(M\) to \(D\), where \(MD=AM\). Prove that triangles \(ABM\) and \(DCM\) are congruent.
Use two pairs of equal segments and vertical angles.
We have \(AM=MD\) by construction, \(BM=MC\) because \(M\) is the midpoint of \(BC\), and \(\angle AMB=\angle DMC\) as vertical angles. Therefore \(\triangle ABM\cong\triangle DCM\) by two sides and the included angle.
Practises the main question after a construction: which triangles became congruent?