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Triangles
Triangles - Revision for Final Exam
| Term | Definition |
|---|---|
| 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
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