Similarity and Review
reflexive property
a shared side or angle; angle C in the figure
corresponding angles
must have parallel lines; make a F
alternate interior angles
must have parallel lines; make a Z
Congruence Symbol
≅
Dilation
A transformation that changes the size of an object, but not the shape.
vertical angles
A pair of opposite congruent angles formed by intersecting lines
Similar Figures
Figures that have the same shape but not necessarily the same size
Congruent figures
Figures that have the same size and shape
SSS~
If the sides of two triangles are in proportion, then the triangles are similar.
AA~
If two pairs of angles in two triangles are congruent, then the triangles are similar.
SAS~
If two pairs of sides are shown to be proportional and the included angles are shown to be congruent in two triangles, then the triangles are similar.
Rigid Motion Transformations
Move the image, but keep the figures congruent Includes: translation, reflection, and rotation
Ways to prove triangles congruent
SSS SAS ASA AAS HL
Ways to prove triangles similar
SSS~ SAS~ AA~
corresponding angles of similar triangles are
congruent
Solving a proportion
cross multiply
corresponding sides of similar triangles are
proportional
Dilations that enlarge a figure
scale factor is greater than 1 examples: 2, 3, 4, 5/2, 2.75, 1.02.....
Dilations that reduce a figure
scale factor is less than 1 examples: 1/2, 1/3, 2/5, 0.25, 0.17, ...
marking proportional sides
there is no marking
Parallel Symbol
|| or arrows on a figure
Similarity Symbol
~
marking congruent sides
use a tick mark
marking congruent angles
use an arc in the angle
You can tell sides are proportional when
you divide the side pairs and get the same number every time.