Math Mini-Flash Cards

Similarity?

Two figures are similar (~) if and only if their corresponding angles are CONGRUENT and their corresponding sides are PROPORTIONAL.

Similarity Statement

Quad. ABC ~ Quad PQRS

Statement of proportionality

AB/PQ = BC/QR = CD/RS = AD/PS

Enlargement

scale factor larger than 1

Reduction

scale factor less than onei

Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimeters is equal to the ration of their corresponding sides lengths. (so like the scale factor for the side lengths is the exact same as the scale factor for the perimeter).

Area of Similar Polygons

If two polygons are similar, then the ratio of their areas is equal to the squares of the ratios of their corresponding sides lengths. ( so like the scale factor for the side lengths SQUARED is the scale factor for area).

5 ways to prove a triangle congruent

• ASA

• SAS

• AAS

• HL

• SSS

Definition of Similar Triangles

All threee angles are congruent and all three corresponding sides are proportional

Three ways to prove triangles similar

• SSS SIMILARITY

• SAS SIMILARITY

• AA SIMILARITY

SSS SImilarity

• All three pairs of sides are proportional.

• To find this: set up all three ratios (of their corresponding sides, ex. AB/PQ, BC/QR), and show they are equal to each other.

AA SImilarity

• Two pairs of congruent angles

• To prove this, have two pairs of congruent angles of two triangles.

• Remember triangle sum th, def of right angles, right angles congruency th

SAS similarity

• Two pairs of proportional sides, and a congruent INCLUDED angle.

Indirect Measurement

We can use similar triangles to solve for missing measures (set up a proportion and solve - remember units of measure)