Mathematics Notes
Analytical Geometry
Length of a line segment:
√(x
y 1 −y 2
1 − x 2 ) 2 + (y 1 − y 2 ) 2
Gradient of a line: m= x 1 −x 2
Midpoint: M= ( x 1 +x 2 y 1 +y 2
2 ; 2 )
Equation of a line: y = mx + c
Parallel lines: m 1 = m 2
Perpendicular lines: m 1 . m 2 = − 1
Angle of inclination:
- Measured in degrees
- From the positive side of the x-axis
- Anti-clockwise direction
- 0° ≤ θ < 180
- If line is horizontal then θ = 0°
- If the line is vertical then θ = 90°
- For a non-vertical line the gradient (m) = tan θ
- Parallel lines have the same angle of inclination
- Perpendicular lines the angles of inclination
Collinear points:
- Two or more points on the same line
- Gradient is the same
, Geometry
Grade 8
- Vert opp angles (equal)
- Angles on a str line (180°)
- Revolution (360°)
At 2 different vertices:
- Alt angles equal AB||CD (z-shape)
- Corresp angles equal AB||CD (F-shape)
- Coint angles equal 180 AB||CD (c-shape)
Triangles
- Angles in a triangle = 180°
- Isos triangle (2 sides and angles =)
- Equilateral triangle (all sides & angles =)
- Ext angles
Congruent Triangles
1. SSS
2. SAS (angle must be between 2 sides)
3. RHS
4. SAA
5. ASS & AAA do not prove congruency
Quadrilateral properties
Square
- Sides are = in length
- Opp sides are ||
- Angles = 90°
- Diags bisect ⊥ and the angles
- Diags are = in length
- Perimeter: 4l
- Area: l 2
Analytical Geometry
Length of a line segment:
√(x
y 1 −y 2
1 − x 2 ) 2 + (y 1 − y 2 ) 2
Gradient of a line: m= x 1 −x 2
Midpoint: M= ( x 1 +x 2 y 1 +y 2
2 ; 2 )
Equation of a line: y = mx + c
Parallel lines: m 1 = m 2
Perpendicular lines: m 1 . m 2 = − 1
Angle of inclination:
- Measured in degrees
- From the positive side of the x-axis
- Anti-clockwise direction
- 0° ≤ θ < 180
- If line is horizontal then θ = 0°
- If the line is vertical then θ = 90°
- For a non-vertical line the gradient (m) = tan θ
- Parallel lines have the same angle of inclination
- Perpendicular lines the angles of inclination
Collinear points:
- Two or more points on the same line
- Gradient is the same
, Geometry
Grade 8
- Vert opp angles (equal)
- Angles on a str line (180°)
- Revolution (360°)
At 2 different vertices:
- Alt angles equal AB||CD (z-shape)
- Corresp angles equal AB||CD (F-shape)
- Coint angles equal 180 AB||CD (c-shape)
Triangles
- Angles in a triangle = 180°
- Isos triangle (2 sides and angles =)
- Equilateral triangle (all sides & angles =)
- Ext angles
Congruent Triangles
1. SSS
2. SAS (angle must be between 2 sides)
3. RHS
4. SAA
5. ASS & AAA do not prove congruency
Quadrilateral properties
Square
- Sides are = in length
- Opp sides are ||
- Angles = 90°
- Diags bisect ⊥ and the angles
- Diags are = in length
- Perimeter: 4l
- Area: l 2
