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Unit 1: Similarity, Congruence, and Proofs Vocabulary Definition Adjacent next to Altitude Perpendicular line from a vertex of a figure to its opposite side; height Angle of Rotation Measure of the angle created by the preimage vertex to the point of rotation to the image vertex Bisector divides into two equal parts Center of Dilation a point through which a dilation takes place; all the points of a dilated figure are stretched or compressed through this point Centroid Point of concurrency of the medians of a triangle Collinear Points points that lie on the same line Complementary sum of the measures of two angles is 90° Compression a transformation in which a figure becomes smaller; compressions may be horizontal (affecting only horizontal lengths), vertical (affecting only vertical lengths), or both Congruent same shape, size, lines, and angles Corresponding sides of two figures that lie in the same position Sides relative to the figure. In transformations, the corresponding sides are the preimage and image sides, so AB and A2Bare corresponding sides and so on. Example Diameter Straight line passing through the center of a circle connecting two points on the circle Dilation a transformation in which a figure is either enlarged or reduced by a scale factor in relation to a center point Enlargement a dilation of a figure where the scale factor is greater than 1 Equidistant Same distance from a reference point Equilateral All sides are congruent Image New, resulting figure after a transformation Inscribe To draw one figure within another so that every vertex of the enclosed figure touches the outside figure Isometry Transformation in which the preimage and image are congruent Line of reflection Perpendicular bisector of the segments that connect the corresponding vertices of the preimage and the image Median of a triangle Segment joining the vertex to the midpoint of the opposite side Midpoint A point that divides a line segment into two equal parts Non Rigid Motion a transformation done to a figure that changes the figure’s shape and/or size Parallel lines that do not intersect Perpendicular lines that intersect to form a right angle. Perpendicular Perpendicular line constructed through the bisector midpoint of a segment Preimage Original figure before undergoing a transformation Point of Point of intersection of concurrent lines (3 or more Concurrency lines that intersect in the same point) Proportion An equation that equates two ratios Radius Line segment that extends from center of a circle to a point on the circle. Length is half the diameter Reduction a dilation where the scale factor is between 0 and 1 Reflection type of transformation that uses a line that acts like a mirror, called the line of reflection, with an image reflected in the line Rigid Motion a transformation done to a figure that maintains the figure’s shape and size or its segment lengths and angle measures Rotation Type of transformation in which a figure is turned about a fixed point, called the center of rotation Scale Factor a multiple of the lengths of the sides from one figure to the transformed figure. If the scale factor is larger than 1, then the figure is enlarged. If the scale factor is between 0 and 1, then the figure is reduced. Similar corresponding angles are congruent and lengths of corresponding sides are proportional Stretch a transformation in which a figure becomes larger; stretches may be horizontal (affecting only horizontal lengths), vertical (affecting only vertical lengths), or both Supplementary sum of the measures of two angles is 180° Translation Type of transformation that maps every two points P and Q in the plane to points P’ and Q’, so that the following two properties are true: PP’ = QQ’, ̅̅̅̅̅ ̅̅̅̅̅ or ̅̅̅̅̅ 𝑃𝑃′ ∥𝑄𝑄′ 𝑃𝑃′ and ̅̅̅̅̅ 𝑄𝑄′ are collinear