Similar Shapes
Triangle Theorems
Ratio & Proportion
Geometric Proofs
Construction & Applications
100

If a polygon's scale factor is r, this is the ratio of the perimeters

What is r?

100

This similarity shortcut only requires two pairs of equal angles
 

What is AA~?

100

if (AD)/(DB)=3/6,

this is the simplified ratio

What is

 1/2?

100

This many pairs of corresponding angles need to be equal to prove triangles similar

 

What is two?

100

This construction is used to divide a line segment into a given ratio


What is the 'Z' construction?

200

When similar polygons have a scale factor of r, their areas have this ratio


What is

r^2

?

200

In SAS~ similarity, this must be included with the proportional sides

What is the included angle?

200

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?

200

To prove SSS~, this must be shown between all corresponding sides


What is proportionality?

200

These lines are essential in the 'Z' construction
 


What are parallel lines?

300

Two similar triangles have areas of 16 and 64 square units. This is their scale factor


What is 2?

300

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?

300

When the scale factor is 4, this is the area ratio


What is 16?

300

These angles are used with parallel lines to prove similarity (2 types)


What are corresponding angles and alternate interior angles?

300

This tool is needed to construct parallel lines


What is a compass and straightedge?

400

This happens to the ratio when you cube the scale factor r

What is the volume ratio of similar 3D shapes?

400

This theorem states that an angle bisector divides the opposite side proportionally to the adjacent sides

What is the Angle Bisector Theorem?

400

If two triangles are similar with sides 5 and 15, this is the ratio of their perimeters


What is

1/3 ?

400

This concept is key in proving the Triangle Proportionality Theorem


What is parallel lines create proportional segments?

400

This number of parallel lines is needed for the generalized Triangle Proportionality Theorem


What is three?

500

To prove polygons are similar by "brute force," you must check this many conditions

What is all corresponding angles and sides?

500

When three parallel lines intersect two transversals, this relationship exists between segments
 

What is proportionality?

500

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 ?


500

This must be proven before using the converse of the Triangle Proportionality Theorem

What is the segments are proportional?

500

This method is used to construct an angle bisector
 

What is the compass method creating equal arcs?