Triangles ACB and DFE are shown below.
Complete the flow chart proof with missing reasons to prove the given ∆ACB, if c2 = a2 + b2, then ∆ACB is a right triangle.
Which pair of reasons correctly completes this proof?

Question

Triangles ACB and DFE are shown below. 
Complete the flow chart proof with missing reasons to prove the given ∆ACB, if c2 = a2 + b2, then ∆ACB is a right triangle.
Which pair of reasons correctly completes this proof?

anonymous · Answer

attachment

anonymous · Answer

Reason #1 - Definition of a Right Triangle
   Reason #2 - Reflexive Property of Equality
		Reason #1 - Pythagorean Theorem 
   Reason #2 - Reflexive Property of Equality
		Reason #1 - Definition of a Right Triangle
   Reason #2 - Transitive Property of Equality
		Reason #1 - Pythagorean Theorem
       Reason #2 - Transitive Property of Equality

directrix · Answer

Reason #1 - Pythagorean Theorem
       Reason #2 - Transitive Property of Equality
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The reason for  f^2 = d^2 + e^2 is clearly the Pythagorean Theorem.

For the second reason, c^2 = (a^2 + b^2) but (a^2 + b^2) = f^2, so c^2 = f^2 by the Transitive Property of Equality