Download Inductive Reasoning

Congruent Triangles
Day 1
Objective:
Discover shortcuts for determining
congruent triangles
A building contractor has just assembled two massive
triangular trusses to support the roof of a recreation hall.
Before the crane hoists the them into place, the contractor
needs to verify the two triangular trusses are identical.
Must the contractor measure and compare
all six parts of both triangles?
What is the smallest number of parts needed?
One?
Two?
No
Angle - Angle
Angle
Angle - Side
Side
Side - Side
No
Three Parts?
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Side-Angle-Angle (SAA)
Side-Side-Angle (SSA)
Angle-Angle-Angle (AAA)
Side-Side-Side (SSS)
1. Construct triangle ∆ABC on
tracing paper by using the
parts from page 220.
2. Compare with your person on
either side of you.
Do you have identical
triangles?
SSS Congruence Conjecture
If the three sides of one triangle are congruent to the three
the triangles are congruent
sides of another triangle, then ______________________.
Side-Angle-Side (SAS)
1. Construct triangle ∆DEF on
tracing paper from the parts
on page 221
2. Compare with your person
on either side of you.
Do you have identical
triangles?
SAS Congruence Conjecture
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another,
then ________________________.
the triangles are congruent.
Congruencies that work:
Side-Side-Side (SSS)
Side-Side-Angle (SSA)
∆BAD

B
Side-Angle-Side (SAS)
∆BAT
T
D
A
Congruent Triangles
Day 2
Objective:
Discover shortcuts for determining
congruent triangles
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)
NO
Angle-Angle-Angle (AAA)
Is this statement true?
∆MNO

∆PQR
Angle-Side-Angle (ASA)
1. Construct triangle ∆MAT
on tracing paper by using
the parts from page 225.
2. Compare with your person
on either side of you.
Do you have identical
triangles?
ASA Congruence Conjecture
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.
Side-Angle-Angle (SAA)
JK is too short
JK is too long
JK is just right
Reason
BC  YZ Given
Deductive
A  X Given
Reasoning
B  Y Given
C
Third
angle
C  Z
Conjecture
ASA
∆ABC  ∆XYZ Conjecture
Z
Side-Angle-Angle (SAA)
B
A
Y
X
Statement
SAA Conjecture
If two angles and a non-included side of one triangle are
congruent to the corresponding angles and side of another
triangle then __________________________.
the triangles are congruent.
What works andp.what doesn’t?
Side-Angle-Angle (SAA)
YES
YES
Angle-Side-Angle (ASA)
Side-Angle-Side (SAS)
YES
Side-Side-Side (SSS)
YES
Side-Side-Angle (SSA)
Angle-Angle-Angle (AAA)
NO
NO