2pir – Comprehensive Explanation and Detailed Examples

2pir is the circumference of a circle. The circumference (or the perimeter) of a circle is the total length of the circle’s boundary. The circumference is a linear measure, and its units are mostly given as centimeters, meters or inches. A circle is a closed round figure, and all the points on the circle’s boundary […]

y = x Reflection – Definition, Process and Examples

The $boldsymbol{ y = x}$ reflection is simply “flipping” a shape or a point over a diagonal line. Since $ y= x$ reflection is a special type of reflection, it can also be classified as a rigid transformation. Knowing how to reflect over the line $y=x$ will come in handy when graphing functions and predicting […]

Congruent Supplementary Angles – Definition, Measure and Explanation

Congruent supplementary angles are angles that meet two conditions — they are congruent and they are supplementary. These angles share these properties, making them unique angles and important ones to learn when working with applications and problems involving angles and algebra. Congruent supplementary angles are angles that add up to $boldsymbol{180^{circ}}$ and, at the same […]

Cavalieri’s Principle – Definition, Conditions and Applications

The Cavalieri’s Principle relates the volumes of two solids given their cross-sections and heights. This principle is also helpful when comparing the areas of two solids given their respective bases and heights. Understanding Cavalieri’s Principle leads to a wide range of properties shared by two and three-dimensional figures. Cavalieri’s Principle states that when the two […]

Horizontal Shift – Definition, Process and Examples

The horizontal shift highlights how the input value of the function affects its graph. When dealing with horizontal shifts, the focus is solely on how the graph and function behave along the $x$-axis. Understanding how horizontal shifts work is important, especially when graphing complex functions. The horizontal shift occurs when a graph is shifted along […]