Locus: At a Fixed Distance from a LineConsider: Your teacher has placed a strip of tape on the classroom floor which forms a straight line. The teacher gives each student a yard stick and asks that each student stand exactly 3 feet away from the line on…

More Information About Similar FiguresIn mathematics, polygons are similar if their corresponding angles are congruent and the ratio of their corresponding sides are in proportion. Once we know that triangles (or any polygons) are similar, we also know …

Platonic Solids (Regular Solids, Regular Polyhedra)Regular Solids Regular solids (regular polyhedra, or Platonic solids which were described by Plato) are solid geometric figures, with identical regular polygons (such as squares) as their faces, and wit…

Similar TrianglesObjects, such as these two cats, that have the same shape, but do not necessarily have the same size, are said to be “similar“. The mathematical symbol used to denote similar is ~. Definition: In mathematics, polygons are similar if th…

DilationsA dilation is a transformation (notation Dk) that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure. The description of a dilation includes the scale factor (or…

Sectors and Segments of CirclesLet’s review what we know about the area of circles and sectors. Area (circle) = πr2Area of sectors of circle (Sectors are similar to “pizza pie slices” of a circle.) Semi-circle (half of circle = half of area) \(A=\frac …

Locus: At a Fixed Distance from a PointConsider: You are standing in the middle of your classroom. The teacher asks Mike, your classmate, to stand 5 feet away from you. The teacher then asks Carlos, Ashley and Anita to also stand 5 feet away from you. Ca…

SpheresSpheres are three-dimensional closed surfaces.A sphere is a set of points in three-dimensional space equidistant from a point called the center. The radius of the sphere is the distance from the center to the points on the sphere. Spheres are not …

Mid-Segment of a TriangleDefinition: The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle. Properties:The mid-segment of a triangle joins the midpoints of two sides of a triangle such that …

Intuitive Notion of DilationA dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation used to create an image larger than the original is called an enlargement. A dilation used to cr…