📐 Geometry Final Exam
Test your mastery across all geometry units — from angles and triangles to coordinate geometry, transformations, and 3D solids.
⏱ 40 Minutes
✦ 20 Questions
🎯 Multiple Choice
📊 Instant Feedback
Core Concepts
Key Formulas to Memorize
📐 Angles
- Supplementary angles = 180°
- Complementary angles = 90°
- Vertical angles are equal
- Exterior angle = sum of remote interior
- Triangle sum = 180°
🔺 Triangles
- Pythagorean: a² + b² = c²
- Area = ½ × base × height
- Special: 30-60-90 → 1: √3: 2
- Special: 45-45-90 → 1:1:√2
- Similar △: ratios of sides equal
⭕ Circles
- Area = πr²
- Circumference = 2πr
- Arc length = (θ/360) × 2πr
- Sector area = (θ/360) × πr²
- Inscribed angle = ½ central angle
▭ Polygons
- Interior sum = (n−2) × 180°
- Each interior (regular) = (n−2)×180°/n
- Exterior sum always = 360°
- Rectangle area = l × w
- Trapezoid = ½(b₁+b₂)×h
📍 Coordinate Geometry
- Distance = √((x₂-x₁)²+(y₂-y₁)²)
- Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2)
- Slope = (y₂-y₁)/(x₂-x₁)
- Parallel: same slope
- Perpendicular: slopes multiply to -1
📦 3D Solids
- Cylinder V = πr²h; SA = 2πrh+2πr²
- Cone V = ⅓πr²h
- Sphere V = (4/3)πr³; SA = 4πr²
- Prism V = Base area × height
- Pyramid V = ⅓ × Base area × h
KEY RATIOS: sin θ = opp/hyp | cos θ = adj/hyp | tan θ = opp/adj
PARALLEL LINES: alt. interior ∠ equal | co-interior ∠ = 180°
TRANSFORMATION: reflection, rotation, translation, dilation
✦ Worked Example
A right triangle has legs of length 6 and 8. Find (i) the hypotenuse, (ii) the area, and (iii) the perimeter.
(i) c = √(6² + 8²) = √(36 + 64) = √100 = 10
(ii) Area = ½ × 6 × 8 = 24 square units
(iii) Perimeter = 6 + 8 + 10 = 24 units
✦ Worked Example — Circle
A circle has radius 7. Find (i) its area and (ii) circumference. Leave answers in terms of π.
(i) Area = π × 7² = 49π sq units
(ii) Circumference = 2 × π × 7 = 14π units