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Transcript
Lesson 11 Guided Notes Using your Algebra Skills 9 A division. is an expression that compares two quantities by A is a statement of equality between two . Lesson 11.1 Similar Polygons Figures that have the same shape and size are figures. Figures that have the same shape but not necessarily the same size are figures. Two polygons are polygons if and only if the angles are and the sides are proportional. The dilation of a polygon is a non-rigid transformation by a scale factor. The polygon retains its shape, but its size is either increased or decreased by the scale factor. Dilation Similarity Conjecture If one polygon is the image of another polygon under a dilation, then the polygons are . Lesson 11.2 Similar Triangles AA Similarity Conjecture If angles of one triangle are congruent to angles of another triangle, then the triangles are . SSS Similarity Conjecture If the sides of one triangle are proportional to the sides of another triangle, then the two triangles are . SAS Similarity Conjecture If sides of one triangle are proportional to of another triangle and the then the two triangles are . sides , Lesson 11.4 Corresponding Parts of Similar Triangles Proportional Parts Conjecture If two triangles are similar, then the corresponding , and are , . Angle Bisector/Opposite Side Conjecture A bisector of an angle in a triangle divides the opposite side into two segments whose lengths are in the same ratio as the of the two forming the . Mini-investigation Conjectures (pg 590 and pg 591) The altitude to the of a right triangle divides the triangle into two right triangles that are to each other and to the original . The altitude (length h) to the of a right triangle divides the into two segments (lengths p and q), such that p = ? . ? q Lesson 11.5 Proportions with Area and Volume Proportional Areas Conjecture If corresponding sides of two similar polygons or the radii of two circles compare in the ratio m , then their areas compare in the ratio n . are solids that have the same shape but not necessarily the same size. All are similar, but not all cylinders are similar. Two polyhedrons are similar if all their similar and the lengths of their . faces are edges are Two right cylinders (or right cones) are similar if their are . and Proportional Volumes Conjectures If corresponding edges (or radii, or heights) of two similar solids compare in the ratio m , then their volumes compare in the n ratio . Lesson 11.6 Proportional Segments Between Parallel Lines Parallel/Proportionality Conjecture If a line parallel to one side of a triangle passes through the other two sides, then it divides the other two sides . Conversely, if a line cuts two sides of a triangle , then it is to the third side. Extended Parallel/Proportionality Conjecture If two of more lines pass through two sides of a triangle parallel to the third side, then they divide the two sides .