2. 1.Classification: by angles; by sides.
2. Special Lines: Altitude, median, bisector,
mediator.
TRIANGLES
3. Centres of a triangle: Incentre, circumcentre,
centroid, orthocentre.
3. 1.1. Classifying Triangles by Angles
• Acute Triangle
A triangle whose three angles are acute is called an
acute triangle. That is, if all three angles of a triangle
are less than 90°, then it is an acute triangle.
4. 1.1. Classifying Triangles by Angles
• Obtuse Triangle
An obtuse triangle is a triangle that has one obtuse
angle.
5. 1.1. Classifying Triangles by Angles
• Right Triangle
If one angle of a triangle is 90°, then it is a right
triangle.
7. 1.2. Classifying Triangles by Sides
• Equilateral Triangle
A triangle with three congruent sides is called an
equilateral triangle.
8. 1.2. Classifying Triangles by Sides
• Isosceles Triangle
If a triangle has at least two congruent sides, then
the triangle is an isosceles triangle.
9. 1.2. Classifying Triangles by Sides
• Scalene Triangle
A triangle that has no congruent sides is called a
scalene triangle.
10. 2.1. Altitude
• Every triangle has three bases (any of its sides)
and three altitudes (heights). Every altitude is the
perpendicular segment from a vertex to its opposite
side (or the extension of the opposite side)
Three bases and three altitudes for the same triangle.
11. 2.2. Median
• A median in a triangle is the line segment drawn
from a vertex to the midpoint of its opposite side.
Every triangle has three medians. In Figure 5 , E is
the midpoint ofBC . Therefore, BE = EC. AE is a
median of Δ ABC.
12. 2.3. Angle Bisector/ Bisecting
• An angle bisector in a triangle is a segment drawn
from a vertex that bisects (cuts in half) that vertex
angle. Every triangle has three angle bisectors. In
figure below, is an angle bisector in Δ ABC.
15. 3.1. Incentre
•Incenter: The three angle bisectors of a triangle
meet in one point called the incenter. It is the center
of the incircle, the circle inscribed in the triangle.
16. 3.2. Circumcentre
• Circumcentre: The three perpendicular bisectors
of the sides of a triangle meet in one point called the
circumcenter. It is the center of the circumcircle, the
circle circumscribed about the triangle.
17. 3.3. Centroid
• Centroid: The three medians (the lines drawn
from the vertices to the bisectors of the opposite
sides) meet in the centroid or center of mass (center
of gravity).
