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# GOAL: To verify the stability of a roof by using geometry to prove that two triangles are congruent.

OR TRY

Click on link to see the triangle.
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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!

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### 1 Answer by Expert Tutors

Joshua S. | An Astrophysicist Who Teaches Just About AnythingAn Astrophysicist Who Teaches Just About...
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Your URL lacked proper parsing: http://blendedschools.blackboard.com/bbcswebdav/pid-25771833-dt-content-rid-11790399_2/courses/MA.09.GeometryA_conversion.bsn/Imported%20Content/Screen%20shot%202012-04-09%20at%201.29.39%20PM.png

Completing this geometry proof is fairly straightforward once you know the rules for when two triangles are congruent. Generally, we look at conditions of angles (A) and sides (S); three in number. The congruency combinations are as follows:

SSS
SAS
AAS
ASA

If you have any of these three elements congruent in the right order, then the triangles are congruent.

In the triangles you are referencing, the relevant postulate is AAS. Do you see it? One of the key things to realize is that two 90 degree angles make a 180 degree angle. This is a form of the angle addition postulate. After you show that angle ACD and angle ACB are congruent, your job is essentially done.

If you want to be 100% clear, you might consider providing a proof of the AAS postulate. Here's a WyzAnt resource that may help you with this:
http://www.wyzant.com/resources/lessons/math/geometry/triangles/congruent_asa_aas