Construct a triangle similar to a given triangle \(PQR\) with its sides equal to \(\frac{2}{3}\) of the corresponding sides of the triangle \(PQR\) (scale factor \(\frac{2}{3} < 1\))
Construction:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Then, \(P'QR'\) is the required triangle, each of whose side is two - third of the corresponding sides of \(\triangle PQR\).
Answer variants:
Draw a line through \(R'\) parallel to the line \(RP\) to intersect \(QP\) at \(P'\).
Draw a ray \(QX\), making an acute angle with \(QR\) on the side opposite to vertex \(P\).
Locate \(3\) (the greater of \(2\) and \(3\) in \(\frac{2}{3}\)) points. \(Q_1\), \(Q_2\), and \(Q_3\), on \(QX\) so that \(QQ_1 = Q_1Q_2 = Q_2Q_3\).
Construct a triangle \(PQR\) with any measurement.
Join \(Q_3R\) and draw a line through \(Q_2\) (the second point, \(2\) being smaller of \(2\) and \(3\) in \(\frac{2}{3}\)) parallel to \(Q_3R\) to intersect \(QR\) at \(R'\).