Triangle Proportionality Theorem

Triangle Proportionality Theorem: If a line is parallel to one side of a triangle and also intersects the other two sides, the line divides the sides proportionally Statements: 1. Triangle ABC with lines EF parallel to CB 2. Angle AEF is congruent to angle ACB and angle AFE is congruent to ABC 3. Triangle ABC is similar to triangle AFE 4. AE/EC=AB/FB 5. AC=AE+EC;AB=AF+EB 6. AE+EC/EC=AF+FB/FB 7. AE/EC+EC/EC=AF/FB=FB/FB 8. AE/EC=AE/FB Reasons: 1. Given 2. Corresponding Angles Postulate 3. Angle-Angle Similarity Postulate 4. Corresponding Sides of Similar Triangles are Proportional 5. Segment Addition Postulate 6. Substitution Property 7. Separations of Fractions 8. Subtraction Property of Equality