Working with Ratio Segments

Working with Ratio SegmentsPART 1~adapted from Walch Education

Triangle Proportionality TheoremIf a line parallel to one side of a triangle intersects the other two sides of the triangle, then the parallel line divides these two sides proportionally

therefore

The converse is also trueIf a line divides two sides of a triangle proportionally, then the line is parallel to the third sideIf

then

ANDWe can show because of the Side-Angle-Side (SAS) Similarity Statement

Segment Addition Postulate.States that if B is between A and C, then AB + BC = AC.It is also true that if AB + BC = AC, then B is between A and C.

PROPERTIESThe Reflexive Property of Congruent Segments means that a segment is congruent to itself, so

The Symmetric Property of Congruent Segments, if , then .

The Transitive Property of Congruent Segments allows that if and , then

Thanks for watching!~Ms. DambrevilleEtude In C Minor Op. 25 No. 12 - ChopinVladimir Horowitz, @ www.emusic.com. Download, play, burn MP3s @ www.emusic.com.Masters of the Roll, Vol. 1: Piano Music of Rachmaninoff, Saint-Saens/Liszt, Bizet, Schubert/Liszt, Chopin, Horowitz, Tchaikovsky and Liszt/Busoni, track 070Other148904.67 - www.emusic.com/albums/9949/