Introduction

A triangle can be constructed without needing all six of its elements (three angles and three sides). The construction is possible when we have specific combinations of elements that ensure triangle congruency.

Required Elements for Triangle Construction

1. Three Sides (S.S.S)

When all three sides of the triangle are known

Example: Sides of lengths 5cm, 6cm, and 7cm

2. Side-Angle-Side (S.A.S)

Two sides and the included angle between them.

Example: Two sides of 4cm and 5cm with included angle of 60°

3. Angle-Side-Angle (A.S.A)

Two angles and the included side between them.

Example: Two angles of 45° and 60° with included side of 5cm.

4. Right-angled Triangle (R.H.S)

Hypotenuse and one adjacent side.

Example: Hypotenuse of 5cm and one side of 3cm.