Unit 8 - Similar Triangles

Similar polygons

Polygons with the same shape but different size.

Polygons are similar if:

1\.) Corresponding angles are congruent

2\.) Corresponding sides are proportional

Scale factor

The ratio of corresponding sides

If polygons are similar, than their ________ are also proportional

perimeter

Perimeters of Similar Polygons Theorem?

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

Areas of Similar Polygons Theorem

If two polygons are similar, then the ratio of their areas is equal to the squares of the ratios of their corresponding side lengths.

AA\~

Angle-Angle Similarity

SSS\~

Side-Side-Side Similarity

SAS\~

Side-Angle-Side Similarity

Triangle Proportionality Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths.

Parallel Lines and Proportional Parts

If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.

Triangle Angle Bisector Theorem

An angle bisector in a triangle separates the opposite sides into two segments that are proportional to the lengths of the other two sides.

Quadratic formula

x = -(b) ± √(b)² - 4(a)(c)

/ 2(a)