Chapter 7 Flashcards
Triangle Angle Bisector Theorem
An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides
Two-Transversal Proportionlity
If three or more parallel lines intersect two transversals then they divide the transversals proportionally
Similar
Shapes that have the same shape but not necessarily the same size
Similar Polygons
Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional
Similarity Ratio
The ratio of two corresponding linear measurements in a pair of similar figures
Similarity Transformation
Is a dilation or a composite of one or more dilations and one or more congruence transformations.
Angle-Angle (AA) Similarity
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar
Side-Side-Side (SSS) Similarity
If the three sides of one triangle are proportional to the three corresponding side of another triangle, then the triangle are similar
Side-Angle-Side (SAS)
If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, the the triangles are similar
Reflexive Property of Similarity
ABC ~ ABC (Reflexive Prop.
of ~
Symmetric Property of Similarity
If ABC ~ DEF then DEF ~ ABC
Transitive Property of Similarity
If ABC ~ DEF and DEF ~ XYZ, then ABC ~XYZ
Triangle Proportionality Theorm
If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proprtionally
Converse of the Triangle Proportionality Therom
If a line divides two sides of a triangle proportionally, the it is parallel to the third side.
Indirect Measurement
A Method of measuring an object by using formulas, similar figures, and/or proportions
