Pure mathematics is, in its way, the poetry of logical ideas. --- Albert Einstein ...Economics is nothing but Mathematics -Dr.Ahsan Abbass...Symmetry is Ornament of Mathematics-Zulfiqar Ali Mir...Law of Nature are But Mathematical Thoughts of God - Euclid (Father of Geometry)...Mathematics is about Number and pattern among these nos.-Sir Zulfiqar A Mir,... Number Theory is Foundation of Mathematics-Sir Zulfiqar Ali Mir

Sunday 16 October 2011

Properties of an Isosceles Triangle

Definition: A triangle is isosceles if two of its sides are equal.
Theorem: Let ABC be an isosceles triangle with AB = AC.  Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC).  Then




  • Ray AM is the angle bisector of angle BAC.




  • Line AM is the altitude of triangle ABC through A.




  • Line AM is the perpendicular bisector of B




  • Segment AM is the median of triangle ABC through A





  • If |AB| is not equal to |AC| then D is not the midpoint of BC so this method doesn't work. In this case you can use trigonometry. The sine of the angle at B is  |AD|/|AB| and thus http://www.k6-geometric-shapes.com/isosceles-triangle.html
    |AD| = |AB| sin(B)

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