Euclidean Geometry
Properties of triangles, quadrilaterals and circles
Angle Relationships
Key angle facts:
Angles on a straight line add up to 180°.
Angles around a point add up to 360°.
Vertically opposite angles are equal.
Angles in a triangle add up to 180°.
Parallel Lines and Transversals
When a transversal crosses two parallel lines, several angle pairs are formed:
Corresponding angles are equal (F-shape).
Alternate angles are equal (Z-shape).
Co-interior angles are supplementary (add to 180°, U-shape).
Example
Proving Angle Values
Given parallel lines AB ∥ CD, with transversal EF:
If angle AEF = 65°, find angle EFD.
AEF and EFD are co-interior angles.
65° + EFD = 180°
EFD = 180° − 65° = 115°
Triangle Properties
Equilateral triangle: all sides equal, all angles = 60°.
Isosceles triangle: two sides equal, base angles equal.
Scalene triangle: no sides equal.
The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
Note
Remember
Always state the reason for each statement in a geometry proof (e.g. 'angles on a straight line', 'alternate angles, AB ∥ CD'). A proof without reasons is incomplete.
Key Vocabulary
ParallelLines that are always the same distance apart and never meet
TransversalA line that crosses two or more other lines
Corresponding anglesEqual angles in matching positions on parallel lines
Alternate anglesEqual angles on opposite sides of the transversal (Z-shape)
SupplementaryTwo angles that add up to 180°
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