Download Yesterday, you learned 2 shortcuts for proving triangles congruent

Notes 4.5/4.6
Geometry Pre-AP
Yesterday, you learned 2 shortcuts for proving triangles congruent. Use either the SSS or the SAS shortcut
to prove the following triangles congruent.
Statements
Reasons
There are 3 more shortcuts that are valid and can be used to prove two triangles congruent!
Angle-Side-Angle (ASA) Congruence
Postulate
Picture
Congruence Statement
If two angles and the
Included side of one triangle
are congruent to two angles
and the included side of
another triangle, then the
triangles are congruent.
**ASA stands for two angles and the _______________ side.
Example:
1. Determine if you can use ASA to prove  UVX   WVX. Explain!
Also, what transformation takes place to change position from one triangle to the
orientation of the second triangle?
Angle-Angle-Side (AAS) Congruence
Postulate
Picture
Congruence Statement
If two angles and a nonincluded side of one triangle
are congruent to the
corresponding angles and
nonincluded side of another
triangle, then the triangles
are congruent.
Example:
2.
DIG DEEPER:
Is AAS the only way to prove these triangles congruent on the problem above? If not, then what
other conjecture could we use?
Hypotenuse-Leg (HL) Congruence
Postulate
Picture
Congruence Statement
If the hypotenuse and a leg
of a right triangle are
congruent to the hypotenuse
and a leg of another triangle,
then the triangles are
congruent.
 This method of proof CANNOT be used unless you first prove the triangles are Right!
Examples:
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what
else you need to know!
3.  VWX and  YXW
4.  VWZ and  YXZ
Section 4.6
Once we have proven that two triangles are congruent, then we know that every other “piece” of the triangles is
ALSO congruent.
Example: If I know that  ABC   RST by _________, then  A must be congruent to  R also.
A
R
12
B
58º
10
Given: PR bisects
C
S
58º
 QPS and  QRS
Prove: PQ  PS
Given:
Prove:
This is because Corresponding
Parts of Congruent Triangles
are Congruent or
12
YW bisects XZ , XY  YZ
XYW  ZYW
10
T