Angles with Parallel LinesA transversal is a line that intersects two or more lines (in the same plane). When lines intersect, angles are formed in several locations. Certain angles are given “names” that describe “where” the angles are located in relat…

Formulas for Angles in Circles Formed by Radii, Chords, Tangents, SecantsFormulas for Working with Angles in Circles (Intercepted arcs are arcs “cut off” or “lying between” the sides of the specified angles.)There are basically five circle formulas that…

Triangle InequalitiesTheorem 1: The sum of the lengths of any two sides of a triangle must be greater than the third side. If these inequalities are NOT true, you do not have a triangle!Example Suppose we know the lengths of two sides of a triangle, and…

Basic Constructionshttps://www.youtube.com/watch?v=mKXqOklRytQIn geometry, constructions utilize only two tools – the straightedge (an unmarked ruler) and the compass. The CompassCompasses come in a variety of styles. Become familiar with the compass you…

Sum of Interior Angles of a PolygonSum of Interior Angles of a Polygon = 180(n – 2) (where n = number of sides)Let’s investigate why this formula is true. Start with vertex A and connect it to all other vertices (it is already connected to B and E by th…

PolygonsPolygonA polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same number of angles as sides. Polygons can be classified as either convex or concave. A polygon is convex if…

Angles Needed for RotationsTo work with rotations, you need to be able to recognize angles of certain sizes and understand the basic workings of a unit circle. You should be able to recognize and reproduce the approximate size of a right angle (90° angl…

Rules for Dealing with Chords, Secants, Tangents in CirclesTheorem 1: If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other. Intersecting Chords Rule: (segment piece)×(…

CylindersCylinders are three-dimensional closed surfaces.In general use, the term cylinder refers to a right circular cylinder with its ends closed to form two circular surfaces, that lie in parallel planes. Cylinders are not called polyhedra since their…

Locus: Equidistant from Two Intersecting LinesConsider: Indiana Jones (Indy) is searching for a treasure. His treasure map shows a V-shaped canyon formed by two vertical cliffs. The directions state: “Start at the point where the cliffs converge. Walk th…