# Congruent triangles SSS and SAS proofs. Write a 2 column for each of the following problem. No explaining needed just the 2 column proof please.

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1)R.T.P.  `Delta BAD cong Delta DCB` ` `

AB       //    DC                    Given

AB       =     CD                    Given (line segments congruent)

`therefore <ABD = <CDB`              Alternate angles AB // DC

BD         =     BD                    Common line

`therefore Delta BAD cong Delta DCB `             SAS

2) R.T.P. `Delta ABD cong Delta BDC`

BD          =      BD                   Common line

AB          =      BC                   Given equilateral `Delta`

AD         =       DC                  Given equilateral `Delta`

`therefore Delta ABD cong Delta BDC`              SSS

3) R.T.P. `Delta GDC cong Delta GAF`

AG         =       GD                   Given G is midpoint of AD

FG          =      GC                   Given G is midpoint of FC

`angle FGA = angle DGC`            vertically opposite angles

`therefore Delta GDC cong Delta GAF`             SAS

4) R.T.P. `Delta BDC cong Delta BDA`

AB        =       BC                    Given (line segments congruent)

AD        =       DC                    Given (BD bisects AC)

BD        =       BD                    Common side

`therefore Delta BDC cong Delta BDA`            SSS

5) R.T.P. `Delta ECD cong Delta BFA`

`angle DEC = angle ABF`             Given `Delta FGE cong Delta CHB`

GE       =        BH                  Given `Delta FGE cong Delta CHB`

DG       =      HA                    Given (line segments congruent)

`therefore` DE      =      BA                    Shown above

FE        =     BC                    Given  `Delta FGE cong Delta CHB`

FC        =     FC                    Common side

` therefore`    EC       =      BF                     Shown above

`therefore Delta ECD cong Delta BFA`             SAS

Ans:

1) SAS     2) SSS     3) SAS     4) SSS      5) SAS

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