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# Triangles

### Triangles - Revision for Final Exam

TermDefinition
scalene triangle A triangle with 3 different sides
isosceles triangle A triangle with at least 2 equal sides
Regular/equilateral triangle A triangle with 3 equal sides, 60° angles
Median A segment connecting a vertex with the midpoint of the opposite side.
Centroid Intersection point of the three medians. It divides the medians in the ratio 2:1, measured from the vertex
Perpendicular bisector (of a side) Set of points equidistant from the endpoints of the segment
Centre of the circumscribed circle The intersection point of the three perpendicular bisectors. Equidistant from the three vertices.
Angle bisector Set of points having the same distance from the arms of an angle
Centre of the inscribed circle The intersection point of the three interior angle bisectors, equidistant from the sides
Midline/midsegment Segment connecting the midpoints of 2 sides. Half the length and parallel to the opposite side.
Escribed circle Circle touching one side from outside, and the extensions of the other two sides of a triangle
Circumscribed circle Circle containing the three vertices of a triangle
Inscribed circle Circle touching all three sides of a triangle
Height Perpendicular segment dropped from a vertex to the opposite side(line). It can be outside of the triangle if it is obtuse.
Height line Straight line containing the height
Orthocentre The intersection point of the three height lines (acute triangle - inside, obtuse triangle - outside , right triangle - at the right angled vertex)
Area of a triangle (a∙m_a)/2=a* b* sin gamma/2
Area of the right triangle a*b/2=c*m_c/2
Area of a regular triangle (root3)/4 * a^2
Height theorem In a right triangle the height corresponding to the hypotenuse is the geometric mean of the segments it cuts from the hypotenuse
Leg theorem In a right triangle a leg is the geometric mean of its perpendicular projection on the hypotenuse and the hypotenuse
Angle bisector theorem The angle bisector divides the opposite side in the ratio of the adjacent sides
Radius of the circumcircle of a right triangle Half the length of the hypotenuse
Thales' Theorem If the hypotenuse of the right triangle is taken as the diameter of a circle the right angled vertex is on the circumference of the circle.
Created by: Rácz Kinga