Download G-10 Triangle Congruence

G-10 Triangle Congruence
SSS, SAS, ASA, AAS, HL
I can test to see if two triangles are
congruent by identifying, comparing
and contrasting what it means to be
ASA, SAS, SSS, AAS and HL
Don’t Write This!
• In G-09, you proved triangles congruent by
showing that all six pairs of corresponding
parts were congruent.
• The property of triangle rigidity gives you a
shortcut for proving two triangles congruent.
SSS – side, side, side
An included angle is an angle formed by
two adjacent sides of a polygon.
B is the included angle between sides AB
and BC.
SAS – side, angle, side
Caution
The letters SAS are written in that order
because the congruent angles must be
between pairs of congruent
corresponding sides.
An included side is the common side of two
consecutive angles in a polygon. The following
postulate uses the idea of an included side.
ASA – angle, side, angle
AAS – angle, angle, side
HL – Hypotenuse, leg
Example 1a
Example 1b
Example 1c
Example 1d
Example 1e
Example 1f
Example 1g
Example 1h
Example 1i
Example 1j
Example 2a
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
SAS
Example 2b
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
SAS
Example 2c
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
ASA
Example 2d
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
SSS
Example 2e
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
ASA
Example 2f
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
AAS
Example 2g
Determine what single piece of missing
information is needed in order to show the
triangles are congruent using the given postulate.
HL
Example 3a
Given: AB  CD, BC  AD
Prove: ΔABC  ΔCDA
Statement
AB  CD, BC  AD
AC  AC
ΔABC  ΔCDA
Reason
Given
Example 3b
Given: AB  CB, D is the midpt. of AC
Prove: ΔABD  ΔCBD
Statement
Reason
Given
AB  CB
D is the midpt. of AC Given
AD  DC
BD  BD
ΔABD  ΔCBD
Example 3c
Given: JL bisects KLM, K  M
Prove: JKL  JML
Statement
JL bisects KLM
KLJ  MLJ
K  M
JKL  JML
Reason
Given
Given
Reflexive
Example 3d
Given: BF  BC, A  D
Prove: ABF  DBC
Statement
BF  BC, A  D
Reason
Given
AAS
Example 3e
Given: B is the midpt. of AE and CD
Prove: ABD  EBC
Statement
Reason
B is the midpt. of AE and CD Given
AB  BE, DB  BC
SAS