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Geometry Unit 2 Name: 9.1 Geometry Unit 2 Name: _____________________________________ 9.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula A transformation is a change in the Transformation position, size, or shape of a figure The pre-image of the transformation Pre-image is the original figure. The image is the figure after the Image transformation. A rigid motion is a transformation Rigid Motion that preserves size and shape. Geometry Unit 2 Name: _____________________________________ 9.2 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Translation A translation is a rigid motion in which every point is moved the same distance and in the same direction. A directed line segment is the distance and Directed Line Segment direction of the translation. A rhombus is a parallelogram with four Rhombus congruent sides. Geometry Unit 2 Name: _____________________________________ 9.3 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Reflection A reflection is a transformation in which a figure is flipped over a line, called a line of reflection. In a reflection transformation, a line of Line of Reflection reflection is the central line about which a figure produces its mirror image. It is also called the line of symmetry. Reflectional symmetry is a figure that has been Reflectional Symmetry reflected over a line. In a reflection transformation, the central line Line of Symmetry about which a figure produces its mirror image. It is also called the line of reflection. Geometry Unit 2 Name: _____________________________________ 9.4 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Rotation A rotation is a transformation in which each point of the pre-image travels clockwise or counter-clockwise around a fixed point a certain number of degrees. A figure has rotational symmetry if it does not Rotational Symmetry change when undergoing a rotation. The angle of rotational symmetry is the Angle of Rotational smallest angle of rotation, less than 360° , that Symmetry maps a figure onto itself. Geometry Unit 2 Name: _____________________________________ 10.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Composition of A series of two or more transformations Transformation performed on a figure. Geometry Unit 2 Name: _____________________________________ 10.2 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Congruent Figures in which one maps to the other by a composition of rigid motions. Congruent figures have the same measures. Geometry Unit 2 Name: _____________________________________ 11.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Corresponding Parts In congruent figures, the corresponding angles with equal measures and the corresponding sides with equal measures. Geometry Unit 2 Name: _____________________________________ 11.2 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Counterexample An example or case that proves a conjecture or theory wrong. A standard or rule on which a judgment can be Criterion based. Geometry Unit 2 Name: _____________________________________ 11.3 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula SSS If three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent. If two sides and the included angle of one SAS triangle are congruent to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent. If two angles and the included side of one ASA triangle are congruent to the corresponding two angles and the included side of another triangle, then the two triangles are congruent. A point lies on the perpendicular bisector Perpendicular of a segment if and only if it is equidistant Bisector Theorem from the endpoints of the segment. Geometry Unit 2 Name: _____________________________________ 11.4 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula AAS If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non- included side of another triangle, then the triangles are congruent. If the hypotenuse and one leg of a right HL triangle are congruent to the corresponding hypotenuse and leg of another triangle, then the triangles are congruent. Geometry Unit 2 Name: _____________________________________ 12.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Flowchart Proof A concept proof representing a proof, where the boxes show statements and each statement is justified. The connecting arrows show the flow of the logic. Geometry Unit 2 Name: _____________________________________ 13.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Triangle Sum The sum of the measures of the angles Theorem of a triangle is 180° A line, ray or segment added to a Auxiliary Line diagram to help in a proof or in determining the solution to a problem If there is a line and a point not on the Parallel Postulate line, then there is exactly one line through the point parallel to the given line. An angle of a triangle formed by two Interior Angle sides of the triangle. An angle formed by one side of a Exterior Angle triangle and the extension of an adjacent side. Remote Interior An interior angle that is not adjacent Angle to a given exterior angle. The measure of an exterior angle is Exterior Angle equal to the sum of the measures of Theorem the two remote interior angles. Geometry Unit 2 Name: _____________________________________ 13.2 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Isosceles Triangle A triangle with two congruent sides Coincide To correspond exactly. If two sides of a triangle are congruent, then Isosceles Triangle the angles opposite them are congruent. Theorem ( If sides, then angles. ) Geometry Unit 2 Name: _____________________________________ 14.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Altitude of a Triangle A segment from the vertex of a triangle, perpendicular to the opposite side of a triangle (or an extension of the opposite side.) Perpendicular Lines Lines that intersect to form right angles Point of Concurrency A point where three or more lines intersect. Point-Slope Form of a The point-slope form of a line is Line y y1 m(x x1 ) where m is the slope and ( x , y ) is a point on the line. 1 1 System of Equations Two or more equations for which a common solution is sought. Orthocenter The point of concurrency of the altitudes of a triangle. Geometry Unit 2 Name: _____________________________________ 14.2 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Median of a Triangle The segment from a vertex of a triangle to the midpoint of the opposite side. Centroid The point of concurrency of the medians of a triangle Centroid Measure The centroid of a triangle divides each Theorem median into two parts so that the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side. Geometry Unit 2 Name: _____________________________________ 14.3 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Circumcenter The point of concurrency of the perpendicular bisectors of the sides of a triangle. Incenter The point of concurrency of the angle bisectors of a triangle. Circumscribed Circle A circle that contains all the vertices of a polygon. Inscribed Circle A circle drawn in the interior of a polygon and tangent to each side of the polygon. Geometry Unit 2 Name: _____________________________________ 15.1 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Kite A quadrilateral with exactly two distinct pairs of congruent consecutive sides. Midsegment of a A segment whose endpoints are the midpoints Triangle of two sides of a triangle. Geometry Unit 2 Name: _____________________________________ 15.2 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Trapezoid A quadrilateral with exactly one pair of parallel sides. Median of a Trapezoid The segment with endpoints at the midpoint of each leg of the trapezoid. Isosceles Trapezoid A trapezoid with congruent legs. Geometry Unit 2 Name: _____________________________________ 15.3 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Parallelogram A quadrilateral with both pairs of opposite sides parallel. Corollary A statement that results directly from a theorem. Geometry Unit 2 Name: _____________________________________ 15.4 Vocabulary Vocabulary Term Definition / Naming Sketch / Symbol / Formula Rectangle A parallelogram with four right angles. Indirect Proof A proof that begins by assuming the opposite of the conclusion. The assumption is used as if it were given until a contradiction is reached. Rhombus A parallelogram with four congruent sides. Square A parallelogram with four right angles and four congruent sides. .
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