If a polygon's scale factor is r, this is the ratio of the perimeters
What is r?
This similarity shortcut only requires two pairs of equal angles
What is AA~?
if (AD)/(DB)=3/6,
this is the simplified ratio
What is
1/2?
This many pairs of corresponding angles need to be equal to prove triangles similar
What is two?
This construction is used to divide a line segment into a given ratio
What is the 'Z' construction?
When similar polygons have a scale factor of r, their areas have this ratio
What is
r^2
?
In SAS~ similarity, this must be included with the proportional sides
What is the included angle?
In similar triangles, if one triangle's side is 8 and the corresponding side in a similar triangle is 24, this is the scale factor
What is 3?
To prove SSS~, this must be shown between all corresponding sides
What is proportionality?
These lines are essential in the 'Z' construction
What are parallel lines?
Two similar triangles have areas of 16 and 64 square units. This is their scale factor
What is 2?
When a line is parallel to one side of a triangle and intersects the other two sides, this theorem applies
What is the Triangle Proportionality Theorem?
When the scale factor is 4, this is the area ratio
What is 16?
These angles are used with parallel lines to prove similarity (2 types)
What are corresponding angles and alternate interior angles?
This tool is needed to construct parallel lines
What is a compass and straightedge?
This happens to the ratio when you cube the scale factor r
What is the volume ratio of similar 3D shapes?
This theorem states that an angle bisector divides the opposite side proportionally to the adjacent sides
What is the Angle Bisector Theorem?
If two triangles are similar with sides 5 and 15, this is the ratio of their perimeters
What is
1/3 ?
This concept is key in proving the Triangle Proportionality Theorem
What is parallel lines create proportional segments?
This number of parallel lines is needed for the generalized Triangle Proportionality Theorem
What is three?
To prove polygons are similar by "brute force," you must check this many conditions
What is all corresponding angles and sides?
When three parallel lines intersect two transversals, this relationship exists between segments
What is proportionality?
In the angle bisector theorem, if the adjacent sides are 6 and 12, this is the ratio of the segments on the opposite side
What is
1/2 ?
This must be proven before using the converse of the Triangle Proportionality Theorem
What is the segments are proportional?
This method is used to construct an angle bisector
What is the compass method creating equal arcs?