The first song is "Beautiful" by Meshell Ndegeocello. It was used in a SYTYCD performance by Chelsie Hightower (now known on Dancing With the Stars) and Mark Kanemura. They are one of my favorite couples in SYTYCD history, and I think this was one of their first performances together.
The next song is "Bloodstream" by Stateless. I'd never heard of the song or the artist until I found this video of a contemporary dance performance by Kathryn McCormick and Cody Green. Kathryn is my favorite female dancer from all the seasons of SYTYCD, and I first saw Cody Green as the lead in the touring production of Broadway's "Movin' Out." This performance is smoking hot! And I totally fell in love with the song.