This document defines key properties of triangles including: vertices, bases, altitudes, medians, angles, and different types of triangles such as isosceles, equilateral, scalene, right, obtuse, acute, and equiangular triangles. It also defines Heron's formula for calculating the area of a triangle when the lengths of all three sides are known. The document was created by Shreyansh Jain and Varun Israni to explain triangle properties.

1. TRIANGLE AND ITS
PROPERTIES

2. The vertex (plural: vertices) is a
corner of the triangle. Every
triangle has three vertices.

3. The base of a triangle can be any one of
the three sides, usually the one drawn
at the bottom.

4. The altitude of a triangle is the
perpendicular from the base to the opposite
vertex. (The base may need to be extended).
Since there are three possible bases, there
are also three possible altitudes. The three
altitudes intersect at a single point, called
the orthocenter of the triangle.

5. The median of a triangle is a line from a
vertex to the midpoint of the opposite
side. The three medians intersect at a
single point, called the centroid of the
triangle.

6. The three angles on the inside of
the triangle at each vertex.

7. The angle between a side of a
triangle and the extension of an
adjacent side.

8. A triangle which has two of
its sides equal in length.

9. A triangle which has all three of
its sides equal in length.

10. A triangle where all three sides
are different in length.

11. A triangle where one of its interior
angles is a right angle (90 degrees).

12. A triangle where one of the
internal angles is obtuse
(greater than 90 degrees).

13. A triangle where all three internal
angles are acute (less than 90
degrees).

14. A triangle which has all three
interior angles equal (congruent).

15. A method for calculating the area
of a triangle when you know the
lengths of all three sides.

16. MADE BY
SHREYANSH JAIN
VARUN ISRANI
EXPLAINED BY
SHREYANSH JAIN