Constructions of Triangles
Constructing triangles using a compass and ruler based on given measurements is an important practical skill in geometry.
Core concept
To construct a triangle given three sides (SSS), we draw one side, then use a compass to mark arcs from each endpoint for the third vertex.
How it works
To construct a triangle given two sides and the included angle (SAS), we draw one side, construct the given angle, then mark the second side's length.
Why it matters
To construct a triangle given two angles and the included side (ASA), we draw the side, then construct both angles at its endpoints.
Key detail
Practising triangle constructions builds precision and reinforces understanding of triangle properties and congruence criteria.
Exam highlight
Key diagram

Keywords worth remembering
Trending
Most searched
Study resources
Notes & downloads
Quick notes
• SSS construction: draw side, use compass arcs.
• This finds the third vertex.
• SAS construction: draw side, construct angle.
• Then mark second side's length.
• ASA construction: draw side, construct both angles.
• At the side's endpoints.
• Practice builds construction precision.
• It reinforces congruence understanding.