Question

Construct any ΔABC. Construct ΔA'BC' such that AB : A'B = 5 : 3 and ΔABC ∼ ΔA'BC'.

Answer 1

Steps of construction:

1. Draw ΔABC in any size.
2. Extend the AB and CB rays.
3. Segment AB should be divided into 5 equal sections.
4. Measure one equal part (of segment AB) on the compass and draw three arcs on extended ray AB beginning at point B.
5. A' represents the intersection of the third arc and the extended ray AB.
6. Draw a line parallel to AC from A'.
7. C' is the point of intersection of this line and the extended ray CB. As a result, ΔA'BC' is the needed triangle, which is comparable to ΔABC.