learning basic geometry definitions

Fundamental concepts of Geometry..

Basic Proportionality Theorem - A line parallel to one side of a triangle divides the other two sides into parts of equal proportion. In triangle ABC, a line drawn parallel to BC cuts AB and AC at P and Q respectively. Let the point P divide AB in the ratio of l: m where l and m are natur..

Point : It is an exact location. It is a fine dot which has neither length nor breadth nor thickness but has position i.e., it has no magnitud..

A line parallel to one side of a triangle divides the other two sides into parts of equal proportio..

Axioms : The self-evident truths or the basic facts which are accepted without any proof are called axiom..

A statement whose validity is accepted without proof is called a postulate. In addition to point, line plane etc, it is also necessary to start with certain other basic statements that are accepted without proof. In geometry these are called postulates. A postulate, though itse..

Introduction - We have studied so far about equalities in a triangle. In an isosceles triangle two of the sides are equal. In an equilateral triangle all the sides are equal. But there exist several situations where we need to compare quantities which are not equal. This gives rise to the concept o..

Midpoint Theorem The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side. Converse of mid point theorem - The straight line drawn through the mid point of one side of a triangle, parallel to another, bisects the third side. The Inte..

Question: Prove mid-point theorem from converse of Basic Proportionality Theorem. [2 Mark] Answer: Given: D and E are the mid-points of AB and AC respectively of a triangle ABC. To prove: DE||BC Proof: .... (1) (Since D is the mid-point of AB, AD = DB) From (1) and ..

Question: If in a D ABC, DE||BC as shown in the figure. [3 Mark] Show that i. ii. Answer: If DE||BC (given) ... (1) (by basic proportionality theorem) Adding 1 on both sides,..