Tangents and CirclesA tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. If you spin an object in a circular orbit and release it, it will travel on a path that is tangent to the circular orbit.Theo…

Negation of Compound Statements and ALL / SOMEWe know that the negation of a true statement will be false, and the negation of a false statement will be true. But what happens when we try to negate a compound statement?Negating a Conjunction (and) and a …

Intuitive Notion of Line ReflectionA reflection can be seen in water, in a mirror, or in a shiny surface. An object and its reflection have the same shape and size, but the figures face in opposite directions. In a mirror, for example, right and left are…

Parallel – Through a PointParallel – through a pointGiven: Point P is off a given line Task: Construct a line through P parallel to the given line. Directions:With your straightedge, draw a transversal through point P. This is simply a straight line whi…

Circles and ChordsA chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.Theorems: In a circle, a radius perpendicular to a chord bisects the chord. In a circle, a radius that bisects a chor…

Intuitive Notion of Rotational  SymmetryAn object has rotational symmetry if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same. The number of positions in which the object looks …

Exterior Angles of TriangleTheorem: An measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (non-adjacent interior angles may also be referred to as remote interior angles)An exterior an…

Theorems Relating Lines and PlanesConsider the following theorems relating lines and planes.  A diagram is supplied for each theorem that represents one possible depiction of the situation.If a line is perpendicular to each of two intersecting lines at t…

Intuitive Notion of Point SymmetryPoint symmetryPoint symmetry exists when a figure is built around a single point called the center of the figure. For every point in the figure, there is another point found directly opposite it on the other side of the …

Bisect a Line Segment and an AngleBisect – cut into two congruent (equal) pieces.Bisect a line segment(Also known as Construct a Perpendicular Bisector of a segment) Given: (Line segment) \(\overline { AB }\). Task: Bisect \(\overline { AB }\)Directions…