Proving Triangles Similar

Definition of similar polygons

Corresponding <s are congruent and the lengths of corresponding sides are proportional

AA~

If 2 <s of one 🔺 are congruent to 2 <s of another 🔺, then the 2 🔺 are ~.

If 2 polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding sides

If 2 polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding sides.

Scale factor

If 2 polygons are ~, then the ratio of the lengths of 2 corresponding sides is called the _______________.

If 3 parallel lines intersect two transversals, then they divide the transversals proportionally.

If 3 || lines intersect 2 transversals, then they divide the transversals proportionally.

Triangle proportionality converse theorem

If a line divides 2 sides of a 🔺 proportionally, then it is || to he third side.

Triangle proportionality theorem

If a line || to one side of a 🔺 intersects the other 2 sides, then it divides the two sides proportionally.

If a ray bisects an angle of a triangle, then it divides the opposite into two segments who's lengths are proportional to the lengths of the other two sides

If a ray bisects an < of a 🔺, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

SAS~

If the lengths of the 2 corresponding sides of 2 🔺 are proportional and the included <s are congruent, then the 🔺 are ~.

SSS~

If the lengths of the corresponding sides of two 🔺 are proportional, then the 🔺 are ~.