SOLUTION: Write a paragraph proof. Given: measure of angle GFI = measure of angle HFJ Prove: measure of angle GFH = measure of angle HFI

Algebra ->  Geometry-proofs -> SOLUTION: Write a paragraph proof. Given: measure of angle GFI = measure of angle HFJ Prove: measure of angle GFH = measure of angle HFI      Log On


   

Question 173843This question is from textbook geometry
: Write a paragraph proof.
Given: measure of angle GFI = measure of angle HFJ
Prove: measure of angle GFH = measure of angle HFI This question is from textbook geometry

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
this is the vertical angle theorm. I am assuming in the prove part that you made a typo and that it should be GFH=JFI not GFH=HFI...I am writing this based on that assumption. If this is not correct you are somehow going to have to let us know what this picture looks like.
:
A straight line is 180 degrees making GJ a 180 degree angle. GFI+JFI=180 degrees and GFH+HFJ=180 degrees by the partition postulate which states that the whole is equal to the sum of the parts. GFI congruent to HFJ is given. HFJ+JFI=180 by substitution (GFI=HFJ)
HFJ+JFI=HFJ+GFH by transitive property. Therefore, JFI is congruent to GFH by the subtraction Postulate.