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.