Two figures are said to be similar if all their corresponding sides are congruent and corresponding angles are equal. By using several copies of the figure below construct a bigger figure that is similar.
It is easy to construct one equilateral triangle from three identical matches. Can we make four equilateral triangles by adding just three more matches identical to the original ones?
Construct a straight line passing through a given point and tangent to a given circle.
Three segments whose lengths are equal to \(a, b\) and \(c\) are given. Construct a segment of length: a) \(ab/c\); b) \(\sqrt {ab}\).
Construct the triangle ABC by the medians \(m_a, m_b\) and \(m_c\).
Construct a triangle with the side \(c\), median to side \(a\), \(m_a\), and median to side \(b\), \(m_b\).
Construct a triangle with the side \(a\), the side \(b\) and height to side \(a\), \(h_a\).
Inside an angle two points, \(A\) and \(B\), are given. Construct a circle which passes through these points and cuts the sides of the angle into equal segments.
Two segments \(AB\) and \(A'B'\) are given on a plane. Construct the point \(O\) so that the triangles \(AOB\) and \(A'OB'\) are similar (the same letters denote the corresponding vertices of similar triangles).
Using a right angle, draw a straight line through the point \(A\) parallel to the given line \(l\).