PROOFS OF SOME BASIC THEOREMS

CONTENT

1. Introduction to Geometry
2. Interior and Exterior Angles of a Triangle
3. Congruency and Similarity of Triangles

Introduction to Geometry

Geometry is the study of the properties of shapes. In theoretical or formal geometry the facts are proved for general cases by a method of argument or reasoning rather than by measurement. Geometrical basic facts are called theorems. Theorems are the foundations upon which geometry is built.

Interior and Exterior Angles of a Triangle

Recall: Angles on a straight line is 180^o. Thus, 

\(θ+50+60=180 \\ θ=180 -110 = 70^o\)

Using the diagram below;

1. Use the angle properties related to parallel lines to explain why;

(a) Angle TRS = angle PQR corresponding or ‘F’ angles

(b) Angle TRP = angle QPR. Alternate or ‘z’ angles

2. Explain why the sum of the three angles at R is 180^o. Angles on a straight line

Theorem: The sum of the angles of a triangle is 180^o

Given: any ΔABC

To prove: \(\hat{A}+\hat{B}+\hat{C}=180^o\)

Construction: Produce (\(\overline{BC}\)) to a point X.