#### Transcript of 5.02 Module Five Quiz

**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

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