18. Lines, Angles & Triangles
Two distinct points can be connected by a single straight line. Three distinct points define a plane.
Coplanar (i.e. lying in the same plane) lines either intersect, or are parallel.
Non-parallel, non-intersecting lines are called skew lines. These are non-coplanar as well.
When two lines intersect, they form an angle (more than one actually, see figure below) between them.
The figure indicates some important math facts about angles.


A triangle is a 3-sided figure. It has three points called vertices where its sides meet.
The sum of the interior angles of a triangle = 180°
Triangles can be of different types:
1. equilateral triangles have all sides and all angles equal. So each interior angle measures 60°
2. isosceles triangles have two sides and their two opposite angles equal.
3. scalene triangles have all sides and all interior angles unequal to all other sides and angles respectively.
4. right angled triangles have one angle that measures 90° - both isosceles and scalene triangles can be right angled triangles.
   sometimes right angled triangles are also called right triangles.

Two triangles are congruent if their corresponding sides and angles measure exactly the same.
Two triangles are similar to each other if:
1. the ratio of their corresponding sides is exactly the same, and
2. their corresponding angles are exactly equal to each other.

Perimeter of a Triangle= sum of lengths of all three sides = a+b+c where a, b, c are the lengths of the three sides.
Area of a Triangle=$1/2$*base*height= Ãs(s-a)(s-b)(s-c) where $s=(a+b+c)/2$. The area formula in terms of s is called Heron's Formula.
For equilateral triangles of side s, Area=$Ã3/4s^2$, Perimeter=$3s$

 


By continuing to use this website, you acknowledge that this service is provided as is, with no warranty of any kind whatsoever.
Copyright 2015 ChiPrime. All rights reserved.