📏 Geometry & Congruence
Geometry questions test your knowledge of angle properties, triangle theorems, polygon rules, congruence, similarity, and transformations. The most important thing in geometry is to always state the property or theorem you are using — marks are awarded for reasoning, not just the final answer.
Geometry in O-Level E-Math is about knowing a toolkit of angle properties and applying them systematically. Most questions involve finding unknown angles by applying 2-3 properties in sequence. The key to success is recognising which property to use, applying it correctly, and stating it clearly in your working.
Angle Properties of Lines
These are the foundational angle properties. You must memorise them and be able to quote them precisely. Examiners look for the exact property name in your working, so do not just write "angles add up" — write the specific property such as "angles on a straight line sum to 180 degrees".
Essential Angle Properties
Angles on a straight line
Sum to 180 degrees. Two or more adjacent angles that together form a straight line always add up to 180 degrees.
Vertically opposite angles
Are equal. When two straight lines intersect, the opposite angles formed are always equal.
Angles at a point
Sum to 360 degrees. All angles around a single point add up to one complete revolution.
Alternate angles (Z-angles)
Equal when lines are parallel. Look for the Z-shape (or S-shape) between two parallel lines cut by a transversal.
Corresponding angles (F-angles)
Equal when lines are parallel. Look for the F-shape between two parallel lines cut by a transversal.
Co-interior angles (C/U-angles)
Sum to 180 degrees when lines are parallel. Same-side interior angles between parallel lines.
Angles on a straight line
Vertically opposite angles
Angles at a point
Alternate angles (Z-angles)
Corresponding angles (F-angles)
Co-interior angles (C-angles)
Triangle angle sum (180°) and exterior angle theorem
📐Angle Properties
Fundamental angle relationships for lines, triangles, and polygons.
\text{sum} = 180°\text{sum} = 360°\text{are equal}\text{are equal (parallel lines)}\text{are equal (parallel lines)}\text{sum} = 180° \text{ (parallel lines)}a + b + c = 180°\text{ext. angle} = \text{sum of two interior opposite angles}📝Worked Example 1: Parallel Lines and Angles
Lines AB and CD are parallel. A transversal crosses them, making angle BAE = 65 degrees at the top line. Find angle DCE at the bottom if angle DCE and angle BAE are co-interior.
Parallel lines AB and CD with a transversal through E and F
📝Worked Example 2: Multi-Step Angle Problem
In the figure, PQ is parallel to RS. Angle QPT = 42 degrees and angle TRS = 75 degrees. Find angle PTR.
PQ is parallel to RS with point T between the lines
What the full chapter covers
Angle Properties of Lines
Polygon Angle Properties
Congruence & Similarity
Similarity: Length, Area, Volume Ratios
Symmetry & Transformations
Proving Congruence in Exam Questions
Properties of Special Quadrilaterals
Describing Transformations Fully
AAA Does NOT Prove Congruence!
Geometry Exam Strategy
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