Reflection in a LineA reflection over a line k (notation rk) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side o…

ContrapositiveThe contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. In other words, the contrapositive negates and switches the parts of the sentence. I…

Locus: Equidistant from Two Parallel LinesConsider: During your morning jog, you run down an alley between two buildings which are parallel to one another and are 20 feet apart. Describe your path through the alley so that you are always the same distan…

Quadrilateral FamilyEach member of the quadrilateral family will describe its specific properties.QuadrilateralI have exactly four sides.The sum of the interior angles of all quadrilaterals is 360º. A quadrilateral is any four sided figure. Do not assum…

Strategies for Dealing with Similar TrianglesTriangles are similar if their corresponding (matching) angles are congruent (equal in measure) and the ratio of their corresponding sides are in proportion.There are many different types of problems that invo…

PyramidsPyramidsPyramids are three-dimensional closed surfaces. The one base of the pyramid is a polygon and the lateral faces are always triangles with a common vertex. The vertex of a pyramid (the point, or apex) is not in the same plane as the base. …

TranslationsA translation “slides” an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. A translation creates a figure that is congruent with the origi…

Locus: Equidistant from Two PointsConsider: You are playing a game of paint ball. Two of your friends are hiding behind trees that are 10 feet apart. Where could you possibly stand so that your firing distance to each friend is exactly the same length? …

InverseThe inverse of a conditional statement is formed by negating the hypothesis and negating the conclusion of the original statement. In other words, the word “not” is added to both parts of the sentence.Example: Conditional: “If you grew up in Alas…

Intuitive Notion of RotationA rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions.Amusement rid…