Download included angle

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.
USE SSS  TO EXPLAIN WHY ∆ABC  ∆CDA.
AB  CD and BC  DA
Given
AC  CA
Reflexive
∆ABC  ∆CDA
SSS 
An included angle is
an angle formed by
two adjacent sides of
a polygon.
B is the included
angle between
AB & BC
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.
The letters SAS are written in that
order because the congruent angles
must be INCLUDED between pairs of
congruent corresponding sides.
Engineering Application
The diagram shows part of
the support structure for a
tower. Use SAS  to explain
why ∆XYZ  ∆VWZ.
XZ  VZ
YZ  WZ
XZY  VZW
∆XYZ  ∆VWZ
Given
VERTICAL <‘s are 
SAS .
An included side is the common side
of two consecutive angles in a polygon.
The following postulate uses the idea of
an included side.
When using ASA  , the side must
be INCLUDED between the angles
known to be congruent.
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.
When using AAS  , the sides must
be NONINCLUDED and opposite
corresponding angles.
Use AAS  to prove the triangles 
Given: JL bisects KLM
K  M
Prove: JKL  JML
JL bisects KLM K  M
JL 
JL
KLJ  MLJ
JKL  JML
Given
Reflexive
Def. < bis.
AAS 
When using HL  , you must FIRST
state that there is a RIGHT
TRIANGLE!
Determine if you can use
the HL Congruence Theorem
to prove ABC  DCB.
AC  DB
Given
ABC & DCB are right angles Given
BC  CB
ABC & DCB are rt. s
 ABC   DCB
Reflexive
Def. right 
HL.
WAYS TO PROVE  TRIANGLES
HL