Euclidean Geometry:

Lines in geometry can be straight, curved, or broken, but we focus mainly on straight lines. Two straight lines can be parallel (never meeting, like railway tracks), intersecting (crossing at one point), or perpendicular (meeting at 90 degrees). When two lines meet, they form angles. Angles are measured in degrees and classified as acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (180°), reflex (between 180° and 360°), or complete (360°). Think of the corners of your school building: the walls form right angles where they meet, while the slanted roof creates obtuse angles. Understanding these classifications helps you solve problems involving geometric shapes and their properties effectively.

A polygon is simply a closed shape made up of straight lines. When solving polygon problems, you need to know that the sum of interior angles depends on how many sides the shape has. The formula is (n-2) × 180°, where n is the number of sides. For a triangle, that's (3-2) × 180° = 180°. For a quadrilateral like a rectangle or the shape of a football field, it's (4-2) × 180° = 360°.

Think of a pentagonal building in Lagos—it has five sides, so its interior angles sum to (5-2) × 180° = 540°. When JAMB asks you to find missing angles or work with regular polygons where all sides are equal, just apply this formula and you're halfway there.

Circle theorems help you find angles inside and around circles without measuring. The most important one is that an angle at the centre is twice the angle at the circumference when both angles subtend the same arc. For example, if you're looking at a circular football pitch in Lagos and draw two lines from the edge to the centre, the angle at the middle will always be double the angle formed at the edge by the same arc.

Another key theorem states that angles in the same segment are equal, meaning if two people stand at different points on a circle's edge looking at the same arc, they see the same angle. Also, angles in a semicircle always equal 90 degrees—this is super useful for quick calculations.

Constructing special angles means drawing angles like 90°, 60°, 45°, and 30° using only a ruler and compass—no protractor allowed. This is a core JAMB skill. When you construct a 90° angle, you're creating a perpendicular line. To do this, you draw a line, pick a point on it, then use your compass to mark equal distances on both sides. Next, open your compass wider and draw arcs above the line from both points until they meet. The line from this meeting point to your original point creates your 90° angle.

Think of constructing the corner of a building plot in Lagos—surveyors use these same geometric methods to ensure corners are perfectly square. For 60° angles, you construct an equilateral triangle since all its angles equal 60°.

Angles are the spaces formed where two lines meet at a point. Think of them like the corners of your classroom or the way a door opens. In geometry, we measure these angles in degrees, shown by the symbol °. Common angles you'll encounter include 30°, 45°, 60°, 75°, and 90°.

A 90° angle is a right angle—like the corner of a book or the intersection of two perpendicular roads in Lagos. A 45° angle is half of a right angle, while 60° appears in equilateral triangles where all three corners are equal. These special angles appear frequently in JAMB questions because they have predictable properties that make calculations easier.

The key to mastering these angles is understanding how they combine and relate. For instance, 75° equals 45° plus 30°. When you recognise these relationships, solving geometry problems becomes much faster.