Problem
GEO-B1-M01-P012 A Small Triangle with a Parallel Side
#12
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), \(\angle B=54^\circ\), \(\angle C=62^\circ\). Point \(D\) lies on side \(AC\). Through \(D\), draw a line parallel to \(BC\); it meets \(AB\) at \(E\). Find the angles of triangle \(ADE\).
Since \(DE\parallel BC\), the angles at \(D\) and \(E\) equal angles of the original triangle.
First, \(\angle A=180^\circ-54^\circ-62^\circ=64^\circ\). Since \(DE\parallel BC\), we have \(\angle ADE=\angle C=62^\circ\) and \(\angle AED=\angle B=54^\circ\). Therefore the angles of triangle \(ADE\) are \(64^\circ\), \(62^\circ\), and \(54^\circ\).
Preparation for similarity without using the word “similarity” yet.