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.
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.)