# Complete the following flow proof for a Hypotenuse-Angle Congruence Theorem. Given : segment AC`cong` segment DF, <C `cong` <F, <B and <E are right angles. Prove: `Delta` ABC `cong`...

Complete the following flow proof for a Hypotenuse-Angle Congruence Theorem.

Given : segment AC`cong` segment DF, <C `cong` <F, <B and <E are right angles.

Prove: `Delta` ABC `cong` `Delta` DEF

Thank you for your help.

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### 1 Answer

The proof largely depends on what theorems and postulates you already have. Here are the basic steps you would need:

`bar(AC) cong bar(DF)` Given

`/_C cong /_F` Given

`/_B,/_E` are right angles Given

`/_B cong /_E` All right angles are congruent. (Usually a theorem)

** If you have AAS as a congruence theorem you can stop here -- we have two angles and the non-included side congruent.**

`/_A cong /_D` If two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent.

`Delta ABC cong Delta DEF` ASA (Usually a postulate; though sometimes treated as a theorem. It depends on the text.)