GOAL: To verify the stability of a roof by using geometry to prove that two triangles are congruent.
ROLE: You are the building inspector, with the job of inspecting the roof. The roof must pass inspection before the building can be used.
AUDIENCE: Sports and Entertainment for Youth, Inc. really hopes the building is ready for their grand opening that is scheduled for next week. This building is going to house an indoor sports and entertainment complex for high school students.
SITUATION: Use the information from the drawing of the roof and state your “Givens”. Then write a formal two-column proof, using the theorems and definitions of geometry learned in this unit to:
Prove that triangle ABC is congruent to triangle ADC.
Proving these triangles congruent will confirm the stability of the roof.
PERFORMANCE: State your givens from the drawing. Make statements in a two-column proof format in which each step has a correct justification. Nothing can be assumed unless it is “given” or “proven” using a theorem, postulate, or definition. The result should end in the undisputed proof that triangle ABC is congruent to triangle ADC. After completing this unit, YOU ARE READY to do this!