Homework Help

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

user profile pic

novjb | (Level 1) Salutatorian

Posted July 9, 2013 at 2:01 AM via web

dislike 1 like

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.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 9, 2013 at 2:16 AM (Answer #1)

dislike 1 like

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.)

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes