The Engineers' Conjectures:The engineers are designing a bridge truss, and they need to prove that two triangles inside the truss are congruent.

1. Complete the table to summarize what you know about each engineer's conjecture:(2 points:1 point for each row of the chart)

EngineerConjectureNatalie

Emma

2. Analyze the conjectures. Who do you think is correct, and why? (1 point)

Analyzing the Data

3. Here is a picture of the bridge truss, and the given information:

Fill out the two-column proof to prove thatBEDBEF. You may not need to use all the rows. (5 points)

StatementReason

4. State how you know thatBDFis an isosceles triangle. (2 points)

5. Using the previous problem, fill out the two-column proof thatABDCBF. You may not need to use all the rows. (5 points)

StatementReason

Making a Decision

6. Are the truss trianglesADBandBFCcongruent? Which postulate did you use for your proof? Which engineer was correct? (1 point)

7. Why do you think triangular structures are so stable? (2 points)

8. Here is a sketch of aPratt truss,patented in 1844 by twoBostonrailway engineers, Caleb Pratt and his son Thomas Willis Pratt.

Name two triangles from the Pratt truss in the illustration that you would expect to be congruent. (2 points)