Geometry - Main Topics Covered The CSEC Mathematics syllabus - CSEC Mathematics exam

 Here’s a clear and student-friendly lesson on Geometry for CSEC Additional Mathematics, covering:

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📐 1. Angles

🔹 Types of Angles:

• Acute: less than 90°
• Right: exactly 90°
• Obtuse: between 90° and 180°
• Straight: exactly 180°
• Reflex: more than 180°

🔹 Angle Rules:

• Angles on a straight line = 180°
• Angles around a point = 360°
• Vertically opposite angles are equal
• Alternate angles (Z-shape) are equal
• Corresponding angles (F-shape) are equal
• Co-interior angles (C-shape) add to 180°

Example:
If one angle on a straight line is 120°, the other is:
180°−120°=60°180°−120°=60°

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🔺 2. Triangles

🔹 Types of Triangles:

• Equilateral: all sides and angles equal (60° each)
• Isosceles: two sides and two angles equal
• Scalene: all sides and angles different
• Right-angled: one angle is 90°

🔹 Triangle Angle Rule:

Sum of interior angles = 180°

Example:
If two angles are 50° and 60°, the third is:
180°−(50°+60°)=70°180°−(50°+60°)=70°

🔹 Pythagoras’ Theorem (Right-angled triangle):

a2+b2=c2a2+b2=c2
Where c is the hypotenuse.

Example:
If a = 3, b = 4, then:
c=32+42=9+16=25=5c=32+42​=9+16​=25​=5

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🟠 3. Circles

🔹 Key Parts:

• Radius: center to edge
• Diameter: across the circle (2 × radius)
• Circumference: distance around the circle
• Chord: line joining two points on the circle
• Tangent: touches the circle at one point
• Arc: part of the circumference
• Sector: “pizza slice” of the circle

🔹 Circle Formulas:

• Circumference:
  C=2πrC=2πr
• Area:
  A=πr2A=πr2

Example:
If radius = 7 cm:

• Circumference = 2×π×7≈44cm2×π×7≈44cm
• Area = π×72≈154cm2π×72≈154cm2

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🧠 4. Geometric Reasoning

This involves using known facts and logic to solve problems.

🔹 Example Problem:

In a triangle, angle A = 40°, angle B = 60°. Find angle C.

Solution:
Use the triangle angle rule:
C=180°−(40°+60°)=80°C=180°−(40°+60°)=80°

🔹 Proofs and Reasoning:

You may be asked to justify why two angles are equal using terms like:

• “Vertically opposite angles are equal”
• “Angles in the same segment are equal”
• “Base angles of an isosceles triangle are equal”