Triangle Constructions

Understanding Triangle Constructions

• Recognise the language and notation of triangle constructions, including terms like bisect (cutting into two equal parts), angle, side, vertex, base, height, and hypotenuse.
• Understand the process of constructing a triangle given three sides (SSS) – you will often use a compass and straightedge for this, beginning with the longest side.
• Be familiar with the method of constructing a triangle when two sides and the included angle (SAS) are provided. Remember that it’s important to first draw one of the sides, and then construct the given angle at one end of this line using a compass.
• Learn how to construct a triangle when two angles and a side (ASA or AAS) are given. Know that you start by drawing the given side, and then construct the given angles at each end of this line.
• Practice creating accurate triangle constructions, as precision is necessary in this topic.

Properties of Triangle Constructions

• Apprehend that congruent triangles are triangles that are identical in every way – they have exactly the same size and shape. Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are of the same measure.
• Understand the conditions for triangle congruence, including Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Right-Angle-Hypotenuse-Side (RHS).
• Know how to prove that two triangles are congruent using the above conditions.

Using Triangle Constructions in Proofs

• Familiarise yourself with geometrical proofs that involve triangle constructions. These could include proving lines parallel, angles equal, or sides equal.
• Recognise that triangle constructions often form the basis of loci and construction problems, where you’re tasked to find a set of points that satisfy certain conditions.