What is a ProofA proof is a written account of the complete thought process that is used to reach a conclusion. Each step of the process is supported by a theorem, postulate or definition verifying why the step is possible. In formal Euclidean proofs, n…

ConesCones are three-dimensional closed surfaces.In general use, the term cone refers to a right circular cone with its end closed to form a circular base surface. The vertex of the cone (the point) is not in the same plane as the base. Cones are not ca…

Theorems Dealing with TrapezoidsTrapezoidDefinition: A trapezoid is a quadrilateral with exactly one pair of parallel sides.Trapezoid has only one set of parallel sides. [The median of a trapezoid is parallel to the bases and equal to one-half the sum o…

Translations and VectorsAnother way to describe a translation is with the use of a vector. A vector is a quantity that has magnitude (length) and direction.A vector is represented by a directed line segment, which is a segment with an arrow at one end in…

Theorems Dealing with Rectangles, Rhombuses, SquaresRectangleDefinition: A rectangle is a parallelogram with four right angles. Properties:Rectangle has all of the properties of the parallelogram.4 right anglesdiagonals congruentUsing the definition, the…

Numerical Work with BIG CirclesA BIG circle question combines all (or most) of your circle angle formulas into one question. You may also need to apply other strategies to find all of the missing angles.Question: Solution: Find the arcs. Then find the…

Styles of ProofA proof is a logical argument that establishes the truth of a statement.Proofs are essential to mathematical inquiry. They are the means by which we can assert that we know that a mathematical concept is true. Author (and mathematician) L…

Arcs in CirclesAn arc is part of a circle’s circumference.Definition: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. Definition: In a circle, the length of an arc is a portion of the circu…

Warm Up Related ConditionalsPeople will often “twist words around” in an attempt to win an argument. In order to avoid becoming a victim of such tactics, you need to be aware of three new conditionals and their related truth values. Each of these new con…

Isosceles Triangle TheoremsAn isosceles triangle is a triangle with two congruent sides. Theorem: If two sides of a triangle are congruent, the angles opposite them are congruent. Theorem: (converse) If two angles of a triangle are congruent, the sides o…