Download Geometry Section 5.7 Using Congruent Triangles

Geometry Section 5.7
Using Congruent Triangles
What you will learn:
1. Use congruent tringles
2. Prove constructions
Since congruent polygons have exactly the
same size and shape, it stands to reason that
corresponding parts of congruent triangles
must be congruent (CPCTC). So if you can
prove two triangles congruent, you can then
state that any pair of corresponding angles or
sides are congruent and use CPCTC as the
reason.
1) FE  ET , UT  ET , F  U , FE  UT
1)Given
2)E & T are right angles
2)Def. of Perpendicular
3)E  T
3)Right Angles Cong. Theorem
)FLE  ULT
4)ASA Cong. Theorem
)FLE  ULT
)CPCTC
1)TV  SU , T is the midpoint of SU
1)Given
2)STV & UTV are Rt. angles
2)Def. of Perpendicular
3)Rt. Angles Cong. Theorem
4)Def. of midpoint
5)Reflexive Prop.
6) SAS Congruence Theorem
3)STV  UTV
4) ST  TU
5)VT  VT
)SVT  UVT
)SVT  UVT
)CPCTC
)VT bisects SVU
)Def. of bisects
Recall the steps involved in constructing an angle congruent to
a given angle.
Because we use the same radius on our compass, AC  AB  DE  DF
Because we use the same radius on our compass, BC  EF
ACB  DFE by SSS
A  D by CPCTC
HW: Do the proofs on the back of this page.