Unit Overview
In this unit, you will build on the skills studied in geometry in grade 9 and delve
deeper into the intricate world of geometric reasoning, exploring the elegance and rigour of formal
mathematical proofs. Using only the rules of angles in triangles and parallel lines that you have
already derived, you will uncover the fundamental principles that govern the properties and rela-
tionships of circles, arcs, segments and angles. You will develop your own formal proofs of the Circle
theorems and learn that these theorems, developed over centuries, have stood the test of time and
continue to play a pivotal role in various branches of mathematics and geometry.
The lessons will also provide insights into the history of geometry, looking further into Euclid’s
Elements and possibly exploring some applications from The Book of Lemmas, attributed to
Archimedes. Euclid, the renowned ancient Greek mathematician, meticulously laid out a systematic
approach to geometry, introducing a wealth of theorems, constructions, and proofs. By immersing
yourself in Euclid’s Elements, you will gain a profound understanding of the logical structure and
deductive reasoning behind his geometric arguments.
Through hands-on activities, collaborative discussions, and individual investigations you will
deepen your understanding of formal proofs. They will enhance their critical thinking skills, cul-
tivate logical reasoning abilities, and develop a keen eye for detail as you embark on the exciting
journey of proving geometric theorems. By the end of this unit, you will have expanded their knowl-
edge of Circle theorems and Euclid’s Elements, and honed their skills in constructing clear and
rigorous proofs.
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