When two lines intersect, the angles opposite each other are always equal. 4. Congruence Theorems To prove two triangles are identical, you can use: : Side-Side-Side SAS : Side-Angle-Side ASA : Angle-Side-Angle Geometric Constructions
Geometry is the study of shapes, sizes, and the properties of space. It relies on a logical system where complex ideas are built from simple, proven truths. Fundamental Concepts
: Used only to connect two existing points. Coordinate vs. Euclidean Geometry Geometry: Theorems and Constructions
Theorems are geometric statements that have been proven using logic and previously established truths. 1. Pythagorean Theorem In a right-angled triangle, the square of the hypotenuse (
📍 : Theorems provide the "why" (logic), while constructions provide the "how" (physical representation). When two lines intersect, the angles opposite each
: Finding the exact midpoint of a line. Angle Bisector : Dividing an angle into two equal parts. Perpendicular Lines : Creating a 90∘90 raised to the composed with power intersection.
Geometry begins with "undefined terms" that form the building blocks for everything else: : Locations in space with no size. It relies on a logical system where complex
Constructions are precise drawings created using only two tools: a and a straightedge (a ruler without markings). Core Constructions