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# 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 180o. 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 180o. Angles on a straight line

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

Given: any ΔABC

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

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

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS1 General Mathematics, SS1 General Mathematics Evaluation Questions, SS1 General Mathematics Evaluation Questions Second Term, SS1 General Mathematics Objective Questions, SS1 General Mathematics Objective Questions Second Term, SS1 General Mathematics Second Term
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