Chapters 8.2 - 8.5

4 ways to prove triangles similar:

1. AAA 2. AA 3. SS 4. SAS

Similar polygons are polygons in which:

1. The ratio of the measures of corresponding sides are equal. 2. Corresponding angles are congruent.

There is a 20 ft. flagpole which causes a 25 ft. shadow. Nearby, a telephone casts a 35 ft. shadow. How tall was the telephone pole?

20/25 = x/35 25x = 700 x =28 ft.

Acronym for corresponding sides of similar triangles are proportional

CSSTP

Side-Splitter Theorem:

If a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally.

Angle Bisector Theorem

If a ray bisects an angle of a triangle, it divides the opposite sides into segments that are proportional to the adjacent sides.

Side-Splitter Corollary

If three or more lines are intersected by two transversals, the parallel lines divide the transversals proportionally.

Perimeter Thereom

The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.

Congruent figures are __________ similar.

always

Corresponding angles of similar triangles are __________.

congruent

Corresponding sides of similar triangles are __________.

proportional

Polygons that are similar have the same __________, but not necessarily the same __________.

shape, size

Similar figures are __________ congruent.

sometimes