📐 Concept Review
Key Geometry Concepts & Formulas
Angles
Complementary: a + b = 90°
Supplementary: a + b = 180°
Vertical angles: equal
Linear pair: 180°
Supplementary: a + b = 180°
Vertical angles: equal
Linear pair: 180°
Triangles
Sum of angles: 180°
Exterior angle = sum of 2 non-adjacent interior
Pythagorean: a² + b² = c²
Exterior angle = sum of 2 non-adjacent interior
Pythagorean: a² + b² = c²
Area Formulas
Triangle: ½bh
Rectangle: lw
Parallelogram: bh
Trapezoid: ½(b₁+b₂)h
Circle: πr²
Rectangle: lw
Parallelogram: bh
Trapezoid: ½(b₁+b₂)h
Circle: πr²
Circle
Circumference: 2πr
Central angle = arc
Inscribed angle = ½arc
Tangent ⊥ radius
Central angle = arc
Inscribed angle = ½arc
Tangent ⊥ radius
Parallel Lines
Corresponding: equal
Alternate interior: equal
Co-interior (same-side): 180°
Alternate interior: equal
Co-interior (same-side): 180°
Polygons
Interior sum: (n−2)×180°
Each interior (regular): (n−2)×180°/n
Exterior sum: always 360°
Each interior (regular): (n−2)×180°/n
Exterior sum: always 360°
Coordinate Geometry
Distance: √[(x₂−x₁)²+(y₂−y₁)²]
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
Slope: (y₂−y₁)/(x₂−x₁)
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
Slope: (y₂−y₁)/(x₂−x₁)
3D Solids
Cube volume: s³
Cylinder: πr²h
Cone: ⅓πr²h
Sphere: (4/3)πr³
Cylinder: πr²h
Cone: ⅓πr²h
Sphere: (4/3)πr³
⚡ Must Memorize
- Interior angle sum of polygon = (n − 2) × 180°
- Pythagorean triples: (3,4,5), (5,12,13), (8,15,17)
- Inscribed angle = ½ × intercepted arc
- Two tangents from external point are equal in length
- Vertical angles are always congruent
- Sum of exterior angles of any polygon = 360°
- Midsegment of triangle = ½ × base, parallel to base
- SAS, ASA, SSS, AAS, HL — triangle congruence theorems
📝 Worked Example
Q: A regular hexagon has how many degrees in each interior angle?
Solution: n = 6, Interior sum = (6−2) × 180° = 720°. Each angle = 720° ÷ 6 = 120°
Q: In a right triangle, legs are 9 and 40. Find the hypotenuse.
Solution: c = √(9² + 40²) = √(81 + 1600) = √1681 = 41
Practice Problems 20 Questions