Download SAS and AAS Postulates

Warm Up 5.3
on desk
Do the Daily Quiz 5.2
5.3
ESSENTIAL QUESTION
• How are triangles congruent using
ASA and AAS postulates?
Angle-Side-Angle Congruence
Postulate (ASA)
• If two angles and the included side of
one triangle are congruent to two angles
and the included side of a second
triangle, then the two triangles are
congruent.
Example 1
Determine When To Use ASA Congruence
a.
b.
SOLUTION
a. C  E,
B  F,
and BC  FE.
Use the ASA Congruence Postulate
Then, ∆ABC  ∆DFE.
b. R  Y
and
S  X.
RT  YZ, but are not included between the
congruent angles, so you cannot use the
ASA Congruence Postulate.
Angle-Angle-Side Congruence
Theorem (AAS)
• If two angles and a non-included side
of one triangle are congruent to two
angles and the corresponding nonincluded side of a second triangle,
then the two triangles are congruent.
Example 2
Determine What Information is Missing
What information is needed to show that ∆JKL  ∆NML?
(by AAS Congruence Theorem)
SOLUTION
You are given KL  ML.
Because KLJ and MLN are vertical angles,
KLJ  MLN.
We need to know that J  N.
Example 2
Determine What Information is Missing
Example 3
Decide Whether Triangles are Congruent
Does the diagram give enough information to show
that the triangles are congruent? If so, state the
postulate or theorem you would use.
a.
SOLUTION
a. We know that:
S EF  JH
A E  J
A FGE  HGJ
Yes, we can use the AAS Congruence Postulate
and that ∆EFG  ∆JHG.
Example 3
Decide Whether Triangles are Congruent
b.
We know only that
MP  QN and NP  NP.
You cannot use AAS or ASA!
Neither SSS or SAS!
Because sides aren’t parallel:
Example 3
Decide Whether Triangles are Congruent
c.
Since sides are parallel:
c. A UZW  XWZ alternate interior angles
S WZ  WZ
A UWZ  XZW alternate interior angles
Use the ASA Congruence Postulate to
conclude that ∆WUZ  ∆ZXW.
Example 4
Prove Triangles are Congruent
A step in the Cat’s Cradle string
game creates the triangles shown.
A
Prove that ∆ABD  ∆EBC.
SOLUTION
BD  BC, AD || EC
C
B
D
E
∆ABD  ∆EBC
Statements
Reasons
1. Given
1. BD  BC
2. Given
2. AD || EC
3. Alternate Interior Angles Theorem
3. D  C
4. Vertical Angles Theorem
4.
ABD  EBC
5.
∆ABD  ∆EBC 5. ASA Congruence Postulate
Checkpoint
Decide Whether Triangles are Congruent
Does the diagram give enough information to show that
the triangles are congruent? If so, state the postulate or
theorem you would use.
1.
2.
ANSWER no
3.
ANSWER no
ANSWER yes; AAS
Congruence
Theorem
• Classwork 5.3A
• IXL: continue Skills B4 & B5