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# Geometry/Diagonals and Altitudes

Question
Hello sir

Sir diagnals and altitudes are confusing? Can you please explain me. If possible can you tell me what is the use of diagnals and altitudes.

Thankyou sir

Hi Shilpa,

A diagonal is a line that connects two non-adjacent vertices in a [convex] polygon.  So in a quadrilateral, there are two diagonals, each joining opposite vertices.  Polygons with more vertices have many more diagonals.  For example, these a regular pentagon has two diagonals from each vertex.  Diagonals are used to subdivide polygons.  There are sometimes interesting properties that can be drawn from diagonals.  For instance, quadrilaterals can be classified based on the lengths of their diagonals and the angle at which they intersect.

An altitude is a line that comes from one vertex and is perpendicular to another edge of the polygon.  There is one altitude per edge in a convex polygon.  Note that the altitude need not be within the polygon.  For instance, an obtuse triangle has two altitudes that lie outside the triangle.  Altitudes are often used in calculating the area of a polygon, i.e. the "height" in a "base times height" style calculation.

Regards,
Azeem

Geometry

Volunteer

#### 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.