Mathematic Notes – Introduction to Plane Geometry

Summary:

The note provides an introduction to plane geometry, covering topics such as the classification of triangles, solving for variables in geometric formulas, angles and parallel lines, and similar triangles. The note explains the different types of triangles based on the length of their sides and angles and provides formulas to calculate the perimeter and area of various geometric shapes such as triangles, trapezoids, parallelograms, rectangles, and circles. It also explains the concepts of interior, exterior, alternate, and corresponding angles, and how to find unknown angles using these concepts. Additionally, the note covers the concept of similar triangles and how to identify them using different conditions such as the AAA, SAS, and SSS rules. The note contains several examples and exercises to help readers practice and apply the concepts covered in the note. The title “Introduction to Plane Geometry: Triangles, Formulas, Angles, and Similarity” would be suitable for this note.

Excerpt:

Introduction to Plane Geometry

Plane Geometry

Classification of triangles:
• Scalene: No two sides are equal in length
• Isosceles: two sides are equal in length
• Equilateral: all three sides are equal in length
• Right: one angle is 90°
Pythagorean Theorem: a2 + b2 = c2

Introduction to Plane Geometry

Solving for variable Geometric Formulas:
• Triangle: Perimeter P = a + b + c, Area A = ½ bh;
Hero’s formula for the area of a triangle:
 = 
−

− 
−  where =

+  + 
• Trapezoid: Area A = ½ h(b1 + b2)
• Parallelogram: Area A = bh
• Rectangle: Area A = LW; Perimeter P = 2L + 2W
• Square (Special case of a rectangle): Apply formulae for the rectangle
• Circle:

Diameter d = 2r, Area A = πr2;
Perimeter (Circumference) C = 2πr or πd; Arc length = 
Example Find the circumference and area of the circle with a radius of 10 m.

Solution:
Circumference = 2 = 2 10 m =  
Area =  =  10 m =  100 m  =