Help with Geometry Proofs: Proving Congruent Angles

[ccmath]

Well, I have a take-home quiz and I need help with 6 geometry proofs. It is due tomorrow (Monday) and I honestly have no clue about any of it... here is the first question, please help me!

Homework Statement

Given: Angle ABG is congruent to Angle DEH
Angle GBC is congruent to Angle HEF

Prove: Angle ABC is congruent to Angle DEF

If you need a picture, let me know! Ill make one in paint.

I also need a statement and reason chart to go with it, I know the concept of making one, just need help solving and making the steps!

Homework Equations

The Attempt at a Solution

 

[kevtimc]

ABG and DEH are congruent
GBC and HEF are congruent

angle ABG = angle DEH
angle GBC = angle HEF

AGB + GBC = DEH + HEF

ABC is congruent with DEF

Can you give reasons why this is?
(Hint: the first is given, the second has to do with properties of congruence)

 

[Architeuthis Dux]

First, we can draw a diagram to represent the given information:

A_______B
/ \
/ \
G_______C_______E
\ /
\ /
D_______F

Statement | Reason
--------------------------------------------------
1. Angle ABG is congruent to Angle DEH | Given
2. Angle GBC is congruent to Angle HEF | Given
3. Angle ABG + Angle GBC = Angle ABC | Definition of Angle Addition
4. Angle DEH + Angle HEF = Angle DEF | Definition of Angle Addition
5. (Angle ABG + Angle GBC) = (Angle DEH + Angle HEF) | Substitution Property of Equality
6. Angle ABC = Angle DEF | Transitive Property of Equality

Therefore, Angle ABC is congruent to Angle DEF by the Transitive Property of Equality.