Geo: Unit 1 Triangle Similarity

goals

1. determine missing measure in similar triangles 2. Determine the postulate or theorem that proves two triangles are similar.

Converse of the Triangle Proportionality Theorem

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

triangle proportionality theorem

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

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle AD bisects angle A

Triangle Angle Bisector Theorem

If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides

rule

AD/CD = AB/CB

similar figures rules

corresponding sides are proportional, corresponding angles have equal measure

proportion

equation that states that two ratios are equal A:B=C:D -b and c are means -a and d are extremes

Pythagorean Theorem

greek mathematician 2500 years ago a2+b2=c2

side-side-side similarity theorem

if 3 sides are proportional then it is similar

tringle proportionality theorem

if a line parallel to one side of a triangle intersects the other 2 sides, it divides tham proportionally

angle-angle similarity postulate

if two angles are congruent then they are similar

polygon similarity postulate

prove that 3 Paris of corresponding sides are proportional

similar

same shape different size wave line means is similar to -write corresponding vertices in the same order

angle bisector theorem

separates the opposite side into segments that hav the same ratio as the other two sides

similar finding unknowns

set up a proportion to find an unknown

side-angle-side similarity theorem

two sides are proportional and the included angle is congruent it is similar

proportions

upper left/lower left = upper right/lower right