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Geometry/Apex vs Vertex

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Question
In our maths class recently the subject of angles arose with some arguing that where the 2 lines meet is the vertex or apex. Is this so? Are the terms interchangeable? Can a 2D shape have an apex e.g. triangle? Could you clarify the terms vertex and apex please especially in relation to angles?
Jane

Answer
Hi Jane!

A vertex is the intersection point of two lines.
An apex is a "summit point" which may or may not be a vertex.  The point of a cone is not a vertex, but it is an apex.  The top vertex of a pyramid (the one not on the base) can be referred to as an apex, but need not.  A 2D shape can have an apex, although it is never necessary to call it so.  For instance, the vertex of an isosceles triangle where the two equal sides intersect can be called the apex.

In closing, vertices and apices are not interchangeable terms.  Sometimes a vertex is also an apex, but usually not.  Personally, I only use the term apex when talking about a point that is certainly not a vertex, such as the apex of a cone.


Cheers,
Azeem

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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