\section*{Geometry Study Guide: Essential Concepts & Theorems}

Master geometry with our comprehensive study guide covering shapes, angles, theorems, and problem-solving strategies.

\subsection*{Basic Geometric Shapes}

\subsubsection*{Triangles} \begin{itemize} \item Equilateral: All sides equal, all angles 60° \item Isosceles: Two sides equal, two angles equal \item Scalene: All sides different, all angles different \item Right: One 90° angle \end{itemize}

\subsubsection*{Quadrilaterals} \begin{itemize} \item Square: All sides equal, all angles 90° \item Rectangle: Opposite sides equal, all angles 90° \item Parallelogram: Opposite sides parallel and equal \item Trapezoid: One pair of parallel sides \end{itemize}

\subsection*{Important Theorems}

\subsubsection*{Pythagorean Theorem} In a right triangle: $a^2 + b^2 = c^2$ where $c$ is the hypotenuse.

\subsubsection*{Triangle Sum Theorem} The sum of interior angles in any triangle is 180°.

\subsubsection*{Exterior Angle Theorem} An exterior angle equals the sum of the two non-adjacent interior angles.

\subsubsection*{Angle Bisector Theorem} If a ray bisects an angle of a triangle, it divides the opposite side proportionally.

\subsection*{Area Formulas} \begin{itemize} \item Triangle: $A = \frac{1}{2}bh$ \item Rectangle: $A = lw$ \item Square: $A = s^2$ \item Circle: $A = \pi r^2$ \item Trapezoid: $A = \frac{1}{2}(b_1 + b_2)h$ \end{itemize}

\subsection*{Volume Formulas} \begin{itemize} \item Cube: $V = s^3$ \item Rectangular Prism: $V = lwh$ \item Cylinder: $V = \pi r^2h$ \item Sphere: $V = \frac{4}{3}\pi r^3$ \item Cone: $V = \frac{1}{3}\pi r^2h$ \end{itemize}

\subsection*{Problem-Solving Strategies} \begin{enumerate} \item Draw a diagram - Visualize the problem \item Identify given information - List what you know \item Apply relevant formulas - Choose appropriate equations \item Solve step by step - Show your work clearly \item Check your answer - Verify the solution makes sense \end{enumerate}

\subsection*{Keywords} geometry study guide, geometric shapes, theorems, area formulas, volume formulas

\subsection*{Last Updated} July 12, 2025, 05:38 PM +04