Edexcel 4MA1 / 4.1 Geometry
Triangle Properties: The Architect
Master the angle sum property, exterior angles, and triangle classification
The Triangle Tuner
Type: Equilateral
Sum: 60° + 60° + 60° = 180°
The Logic Track
Foundation Rule
All triangles have angles that sum to exactly 180°. This is ALWAYS true.
Isosceles ID Trick
Look for the tick marks on the sides!
If two legs are equal, the base angles (the shoes) are equal too.
Exterior Shortcut
Don't waste time finding the angle on a straight line first!
Jump straight to: Ext = Sum of 2 opposite interior angles
!
Examiner Trap
Students often confuse the interior angle with the exterior angle. Read the question carefully!
Triangle Types
Equilateral: All sides equal → All 60°
Isosceles: Two sides equal → Two angles equal
Scalene: All sides different → All angles different
The Dynamic Solver
Question: An isosceles triangle has a top angle of 40°. Find the base angles.
1
Apply Angle Sum Property
All angles in a triangle sum to 180°
Top + Base₁ + Base₂ = 180°
2
Substitute Known Value
Top angle = 40°, and in isosceles: Base₁ = Base₂
40° + Base + Base = 180°
3
Remove Top Angle
Subtract 40° from both sides
180° - 40° = 140°
2 × Base = 140°
4
Divide by 2
Split remaining angle equally between two base angles
Base = 140° ÷ 2
Base = 70°
✓
Final Answer
Each base angle = 70°
Check: 40° + 70° + 70° = 180° ✓
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