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