Foundations of Euclidean Geometry

Triangle Sum Theorem - Fundamental Rule

Thales' Theorem - Circle Property

In ______ geometry, the examination of ______ is crucial, focusing on ______ and ______ as primary concepts.

Triangles are ______ if they match exactly when laid on top of each other, matching by ______ and ______.

______ between triangles means they have identical ______ but may differ in ______.

To establish ______ of triangles, one can use ______, ______, or ______ methods.

Understanding ______ and solving problems with geometric figures often requires knowledge of these ______ principles.

Angle measurement unit in Euclidean geometry

Calculating area of a rectangle

Determining volume of a rectangular prism

Mechanical engineers apply ______ geometry for stress analysis and designing parts like ______.

In ______ engineering, the stability and safety of structures like buildings and bridges depend on ______ geometry.

Optical engineers use geometric principles to create lenses that properly ______ light.

Navigation systems utilize ______ geometry for tasks such as satellite orbit calculations and planning ______ routes.

Contributions of Archimedes to Euclidean geometry