1. CONGRUENT TRIANGLES

3. How To Find Congruent Sides ? ?
Remember to look for the following:
Adjacent triangles share a COMMON SIDE, so you can apply the REFLEXIVE Property to get a pair of congruent sides.
Look for segment bisectors.. They lead to midpoints…. Which lead to congruent segments.

4. Use SSS  to explain why ∆ABC  ∆CDA.
AB  CD and BC  DA Given
AC  CA Reflexive
∆ABC  ∆CDA SSS 

5. An included angle is an angle formed by two adjacent sides of a polygon.
B is the included angle between

7. How To Find Congruent ANGLES ? ?
Remember to look for the following:
Look for VERTICAL ANGLES.
Look for lines. They form  adjacent angles.
Look for // LINES CUT BY A TRANSVERSAL. They lead to  angles.
Look for < bisectors. They lead to  angles.

8. The letters SAS are written in that order because the congruent angles must be INCLUDED between pairs of congruent corresponding sides.

9. XZY  VZW VERTICAL <‘s are 
Engineering Application
The diagram shows part of the support structure for a tower. Use SAS  to explain why ∆XYZ  ∆VWZ.
XZ  VZ YZ  WZ Given
XZY  VZW VERTICAL <‘s are 
∆XYZ  ∆VWZ SAS .

10. An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

12. When using ASA  , the side must be INCLUDED between the angles known to be congruent.

13. Determine if you can use ASA  to prove NKL  LMN. Explain.
KL and NM are //.
KLN  MNL, because // lines imply  alt int >s.
NL  LN by the Reflexive Property.
No other congruence relationships can be determined, so ASA  cannot be applied.

15. When using AAS  , the sides must be NONINCLUDED and opposite corresponding angles.

16. Use AAS  to prove the triangles 
Given: JL bisects KLM
K  M
Prove: JKL  JML
JL bisects KLM K  M Given
JL  JL Reflexive
KLJ  MLJ Def. < bis.
JKL  JML AAS 

18. When using HL  , you must FIRST state that there is a RIGHT TRIANGLE!

19. Determine if you can use the HL Congruence Theorem to prove ABC  DCB.
AC  DB Given
ABC & DCB are right angles Given
BC  CB Reflexive
ABC & DCB are rt. s Def. right 
 ABC   DCB HL.

20. Ways to prove  triangles
SSS
SAS
HL
ASA
AAS