Geometry and Trigonometry - Complete Interactive Lesson
Part 1: Lines & Angles
📝 Geometry Angles
Part 1 of 7 — Lines and Angles
Vertical angles are equal; linear pair = 180°.
Parallel lines cut by a transversal: corresponding angles equal, alternate interior angles equal.
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Key Insight: Sum of angles in a triangle = 180°.
SAT Tip: Exterior angle = sum of two remote interior angles.
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Part 2: Triangle Properties
Triangles
Part 2 of 7 — Triangles
Pythagorean theorem: a² + b² = c² (right triangles).
Special right triangles: 30-60-90 (x, x√3, 2x) and 45-45-90 (x, x, x√2).
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Key Insight: Triangle inequality: sum of any two sides > third side.
SAT Tip: Similar triangles: corresponding sides proportional, angles equal.
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Part 3: Circle Properties
Circles
Part 3 of 7 — Circles
Area = πr²; Circumference = 2πr.
Arc length = (θ/360) × 2πr; Sector area = (θ/360) × πr².
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Key Insight: Central angle = arc measure.
SAT Tip: Inscribed angle = half the intercepted arc.
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Part 4: Area & Volume
Coordinate Geometry
Part 4 of 7 — Coordinate Geometry
Distance: d = √((x₂-x₁)² + (y₂-y₁)²).
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2).
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Key Insight: Slope: m = (y₂-y₁)/(x₂-x₁).
SAT Tip: Parallel lines: same slope; Perpendicular lines: slopes are negative reciprocals.
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Part 5: Coordinate Geometry
Volume & Surface Area
Part 5 of 7 — Volume & Surface Area
Rectangular prism: V = lwh, SA = 2(lw + lh + wh).
Cylinder: V = πr²h, SA = 2πr² + 2πrh.
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Key Insight: Cone: V = (1/3)πr²h.
SAT Tip: Sphere: V = (4/3)πr³, SA = 4πr².
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Part 6: Problem-Solving Workshop
Problem-Solving Workshop
Part 6 of 7 — Problem-Solving Workshop
Rectangular prism: V = lwh, SA = 2(lw + lh + wh).
Cylinder: V = πr²h, SA = 2πr² + 2πrh.
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Key Insight: Cone: V = (1/3)πr²h.
SAT Tip: Sphere: V = (4/3)πr³, SA = 4πr².
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Part 7: Review & Applications
Review & Applications
Part 7 of 7 — Review & Applications
Rectangular prism: V = lwh, SA = 2(lw + lh + wh).
Cylinder: V = πr²h, SA = 2πr² + 2πrh.
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Key Insight: Cone: V = (1/3)πr²h.
SAT Tip: Sphere: V = (4/3)πr³, SA = 4πr².
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