Chapters 8 & 9 Top 12 Concepts

Definitions

Ratio - two quantities that are measured in the same unit ((inches, feet, yards, etc.))
Scale Factor - the ratio of 2 corresponding sides
Similar Polygons - 2 polygons whose sides are in proportion and whose angles are equal

Postulates/Theorems

Chapter 8 Theorems ((proving triangles are similar))
Angle-Angle Similarity (AA) - if two angles of one triangle are congruent to 2 angles of another triangle, then the two triangles are similar ((NOT CONGRUENT, BUT SIMILAR!!))
Side-Side-Side Similarity (SSS) - if the lengths of the corresponding sides of 2 triangles are proportional, then the triangles are similar ((NOT CONGRUENT, BUT SIMILAR!!))
Side-Angle-Side Similarity (SAS) - if an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are SIMILAR
Chapter 9 Theorems ((using pythagorian theorem))
To find out if the triangle you are looking at is RIGHT, plug the numbers into this equation ----> a² + b² = c². If this statement is true, then you have yourself a RIGHT TRIANGLE!!
To find out if the triangle you are looking at is OBTUSE, plug the numbers given into this formula ----> a² + b² < c². If this statement is true, then the triangle you are looking at is OBTUSE!!
To find out if the triangle you are looking at is ACUTE, plug the numbers given into this equation ----> a² + b² >c². If this statement is true, then the triangle is ACUTE!!
**a = one leg, b = the other leg, c = the hypotenuse

Trigonomic Ratios