Edexcel Mathematics (4XMAF) -Unit 1 - 4.7 Geometrical Reasoning- Study Notes- New Syllabus
Edexcel Mathematics (4XMAF) -Unit 1 – 4.7 Geometrical Reasoning- Study Notes- New syllabus
Edexcel Mathematics (4XMAF) -Unit 1 – 4.7 Geometrical Reasoning- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A give informal reasons, where required, when arriving at numerical solutions to geometrical problems
Notes: reasons only required for geometrical calculations based on lines (including chords and tangents), triangles or polygons
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Geometrical Reasoning
In geometry, you are often asked not only to find an angle, but also to state the reason for each step.
This means explaining which rule you used.
Common Reasons You Must Know
- Angles on a straight line add to \( 180^\circ \)
- Angles around a point add to \( 360^\circ \)
- Vertically opposite angles are equal
- Alternate angles are equal (parallel lines)
- Corresponding angles are equal (parallel lines)
- Co-interior angles add to \( 180^\circ \)
- Angles in a triangle add to \( 180^\circ \)
- Exterior angle of a triangle equals two opposite interior angles
- Isosceles triangle base angles are equal
Key Idea
You must write the reason beside each calculation step.
Example 1:
Two angles lie on a straight line. One angle is \( 120^\circ \). Find the other and state the reason.
▶️ Answer/Explanation
\( 180^\circ – 120^\circ = 60^\circ \)
Reason: Angles on a straight line add to \( 180^\circ \).
Conclusion: \( 60^\circ \).
Example 2:
Two lines intersect. One angle is \( 45^\circ \). Find the vertically opposite angle and give a reason.
▶️ Answer/Explanation
\( 45^\circ \)
Reason: Vertically opposite angles are equal.
Conclusion: \( 45^\circ \).
Example 3:
In a triangle, two angles are \( 70^\circ \) and \( 50^\circ \). Find the third angle and state the reason.
▶️ Answer/Explanation
\( 180^\circ – (70^\circ + 50^\circ) = 60^\circ \)
Reason: Angles in a triangle add to \( 180^\circ \).
Conclusion: \( 60^\circ \).