An altitude of a triangle is a perpendicular line segment from a vertex to the line determined by the opposite side. In [b]△[/b]BCD below, segment BE is the altitude from vertex B to the line containing DC.
How many triangles do you see?
Identify the triangles by name. For example, one triangle is BCD.
BCD, BEC, and BED
Is [color=#ff0000][b]△[/b]BCD[/color] ~ [color=#38761d][b]△[/b]BEC[/color]? If so, name the rule.
Is [color=#ff0000][b]△[/b]BCD [/color]~ [color=#0000ff][b]△[/b]BED[/color]? If so, name the rule.
Is [color=#38761d][b]△[/b]BEC[/color] ~ [color=#0000ff][b]△[/b]BED[/color]? How do we know this to be true?
Since similarity is transitive, [b]△[/b]BCD ~ [b]△[/b]BEC and [b]△[/b]BCD ~ [b]△[/b]BED, then [b]△[/b]BEC ~ [b]△[/b]BED.