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5.02 Module Five Quiz
Transcript of 5.02 Module Five Quiz
Triangle Proportionality Theorem
Given: Triangle DFG, segment EH intersects segment DF and segment DG, and EH || FG.
Prove: DE/DF = DH/DG
1. Triangle DFG is intersected by line EH = Given
2. EH || FG = Given
3. angle DFG is congruent to angle DEH = Corresponding Angles Postulate
4. angle DGF is congruent to angle DHE = Corresponding Angles Postulate
5. Triangle DFG is similar to triangle DEH = Angle-Angle Similarity Postulate
6. DE/DF is equal to DH/DG = Converse of Side-Side-Side Similarity Postulate
Converse of Triangle Proportionality Theorem
Given: Triangle DFG, segment EF intersects segment DF and segment DG, and DE/DF equals DH/DG
Prove: EH || FG
1. DE/DF = DH/DG = Given
2. angle D is congruent to angle D = reflexive property
3. triangle EDH ~ triangle FDG = Side-Angle-Side Similarity Postulate
4. angle DEH is congruent to angle DFG = Corresponding angles of similar triangles are congruent
5. EH || FG = Converse of corresponding angles postulate