Problem
GEO-B1-M07-P006 Construct an Isosceles Triangle
#6
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), ray \(BA\) is extended beyond point \(B\) to point \(D\) so that \(BD=BC\). If \(\angle ABC=52^\circ\), find \(\angle BCD\).
Triangle \(BCD\) is isosceles.
Since \(D\) lies on ray \(BA\), \(\angle DBC=\angle ABC=52^\circ\). In triangle \(BCD\), sides \(BD\) and \(BC\) are equal, so \(\angle BCD=\angle CDB\). Hence \(\angle BCD=\frac{180^\circ-52^\circ}{2}=64^\circ\).
Practises “construct an equal segment — get equal angles”.