Intermediate Geometry explores the properties and relationships of shapes, sizes, and theorems in two and three dimensions.
Triangles are the most basic polygon with three straight sides and three angles. Each triangle's internal angles add up to \(180^\circ\), a rule known as the Triangle Angle Sum Theorem.
The Pythagorean Theorem applies to right triangles and states that: \[ a^2 + b^2 = c^2 \] where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse.
Triangles are used in many fields, such as engineering (truss bridges) and art (design patterns).
Triangles provide structural stability and are found in roof supports, bridges, and sculptures.
\[a^2 + b^2 = c^2\]
A triangle with sides 3, 4, and 5 units is a right triangle because \(3^2 + 4^2 = 5^2\).
Roof trusses use equilateral triangles for strength and balance.
Triangles have unique side and angle properties, with applications in design and engineering.