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Transcript
Accelerated Geometry Geometry Prerequisite Notes Name______________________________ Date_______________________________ Congruent Triangles Vs. Similar Triangles Graphic Organizer Congruent Triangles ( ) Having the same size and shape. All corresponding parts are equal. Similar Triangles ( ) Having the same shape, but not necessarily the same size. All corresponding angles are equal and corresponding sides are proportional. Geometric Transformations Isometries DilationTranslation, Reflection, Rotation Transformation that changes the size of a figure, but not the shape. (x, y) (kx, ky) k is called the scale factor. Proving Triangles Congruent and Similar Term/ Definition/Explanation Term/ Definition/ Diagram Postulate Postulate Explanation If 3 sides of 1 triangle are If the three sides congruent to 3 sides of of one triangle Side – Side another triangle, then the 2 are proportional Side – Side Side triangles are congruent. to the three Side SSS corresponding sides of another SSS triangle, then the ABC DEF triangles are similar If 2 sides and the included If two sides of one angle of one triangle are triangle are congruent to 2 sides and the proportional to Side-Angle-Side included angle of another two sides of Side-Angle-Side SAS triangle, then the 2 another triangle SAS triangles are congruent. and their included ABC DEF angles are congruent, then the triangles are similar. If 2 angles and the included If two angles of side of one triangle are one triangle are congruent to 2 angles and congruent to two Angle – Side the included side of another angles of another ABC DEF Angle- Angle Angle triangle, then the 2 triangle, then the AA triangles are congruent. triangles are ASA similar. Angle-AngleSide AAS If 2 angles and one nonincluded side of one triangle are congruent to 2 angles and one non-included side of another triangle, then the 2 triangles are congruent. Vocabulary Word Complmentary Angles Linear Pair Vertical Angles Adjacent Angles Alternate Interior Angles Corresponding Angles Alternate Exterior Angles Triangle Angle Sum Theorem Exterior Angle Theorem Scalene Triangle Isosceles Triangle Angle Bisectors Incenter Medians Centroid Midsegment Theorem Definition/Rule Illustration/Example