Transcript Triangle Congruence by ASA and AAS 4-3

Triangle Congruence by ASA and AAS
4-3
Objective:
To prove two triangles congruent using the
ASA Postulate and the AAS Theorem.
What works and what doesn’t?
Side-Angle-Side (SAS)
YES
Side-Side-Side (SSS)
YES
Angle-Side-Angle (ASA)
Side-Angle-Angle (SAA)
Side-Side-Angle (SSA)
Angle-Angle-Angle (AAA)
(naughty donkey)
NO
Angle-Angle-Angle (AAA)
Is this statement true?
∆MNO

∆PQR
Which two triangles are
congruent by ASA?
Explain.
We already have pairs of ≅ angles. We have
congruent sides but are they included?
Do congruent sides have
congruence markings (ticks)?
SinceU  E, UV  EO, andV  O,
ΔSUV  ΔNEO
Statement
Angle-Angle-Side (AAS)
Deductive
Reasoning
B
C
A
Y
BC  YZ
A  X
B  Y
Given
C  Z
Third angle
Conjecture
∆ABC  ∆XYZ
X
Z
Reason
Given
Given
AAS Conjecture (and
ASA)
What works and what doesn’t?
4-3 p.238: 1-4, 6, 10,
12, 13, 15-18
Side-Angle-Side (SAS)
YES
Side-Side-Side (SSS)
YES
[Write entire proof
Angle-Side-Angle (ASA) in two columns]
Side-Angle-Angle (SAA)
YES
Angle-Angle-Angle (AAA)
NO
YES
Side-Side-Angle (SSA)
(naughty donkey)
NO