Chapter 11 Similarity, Proportions, SAV Flashcards
Means extremes property
“Cross multiplying”
3x/3=24/3 (short cut of 24/3=8)
9x=72
X=8
Scale factor
The simplified fraction of the extended proportion.
Similar figures
Corresponding angles are congruent, corresponding sides are proportional.
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. (AA) Write the similarity statement.
SAS Similarity
If an angle of one triangle is congruent to an angle of another triangle and the sides INCLUDING those angles are in proportion, then the triangle is similar. (SAS) Write a proportion for the sides to make sure they have the same scale factor.
SSS Similarity
If the three pairs of sides of the two triangles are in proportion, then the triangles are similar. (SSS) Write an extended proportion to ensure they have the same scale factor.
Corresponding parts in Similar triangles
If the two triangles are similar, then the corresponding medians, altitudes, and angle bisectors are proportional to the corresponding sides.
Triangle angle bisector theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into segments promotional to the other two sides.
Sav
Single dimension/length
Scale factor/ratio of perimeters
Can include and single dimension length like a radius or a height.
sAv
Two dimensions
Ratio of surface areas
Can include total area and lateral area
The scale factor squared
saV
Three dimensions
Ratio of volumes
Cube of the scale factor
Triangle Proportionality Theroem
If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
Extended proportion
A proportion with multiple proportions written in one equation.
