Download Day 20a - 5 Triangle Congruence Rules and Non Rules

2
1
2
3
4
5
Similarity, Congruence & Proof
Unit 2 Content Map and Standards
Similarity vs Congruence Transformations (Shutter)
Properties of Algebra (Flip Book)
Properties of Equality (Think Map)
Triangle Congruence Rules & Non Rules (6 door)
Triangle Congruence
Standards:
MCC9-12.G.SRT.5 Use congruence and similarity
criteria for triangles to solve problems and to prove
relationships in geometric figures.
Essential Question:
• Under what conditions are similar figures
congruent?
• How do I know which method to use to prove two
triangles congruent?
Eight Door Foldable
MCC9-12.G.SRT.5
(front – closed)
Can I prove these
triangles congruent?
Side-Angle-Side
(SAS)
Hypotenuse-Leg
(HL)
Angle-Side-Side
(SS)
Note: whole
sheet of
regular paper
landscape
Side-Side-Side
(SSS)
Angle-Side-Angle
(ASA)
Angle-Angle-Side
(AAS)
Angle-Angle-Angle
(AAA)
Can I prove these triangles congruent?
MCC9-12.G.SRT.5
(top left door opened)
Two triangles are congruent if and only if
sides
corresponding __________________
and corresponding
angles
__________________
are congruent.
You only need ___________
three sets of corresponding parts
congruent in order to prove two triangles are
congruent.
correct
Do you have the _________________
information?
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
SSS
(top right door opened)
Three pairs of
congruent
____________________
Y
sides.
_
_E
_S
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
SAS
(second left door opened)
Two pairs of
Y _________________
congruent
sides and the
E
included
_________________
angle.
S
_
_
_
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
ASA
(second right door opened)
Two pairs of
congruent
___________________
angles and the
included
___________________
side.
_Y
_E
_S
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
HL
(third left door opened)
Two pairs of
Y ___________________
congruent
sides of a
E ___________________
right
triangle.
S
_
_
_
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
AAS
(third right door opened)
Two pairs of
congruent
___________________
angles and the
Non-included
___________________
side.
_Y
_E
_S
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
SS
(bottom left door opened)
Triangles may
_N ______
NOT be
congruent.
0
_
_!
NOT prove triangle
**You can ______
Similarity or
__________________
____________________
Congruence with this
postulate.
Closed
Closed
Closed
Closed
Closed
Closed
Closed
MCC9-12.G.SRT.5
AAA
(bottom right door opened)
NOT prove
You can _______
N ___________________.
Congruence
_
0
can
_ Similarity
!
_
**You ________ prove triangular
___________________
(AA Similarity Postulate).
Closed
Closed
Closed
Closed
Closed
Closed
Closed
Summarizer (back – closed)
Compare and Contrast each of the rules for congruence. Also compare them
with the “non-rules” for congruence.
Student Template
• Print next two “Slides” and copy them
double sided
Side-SideSide
(SSS)
Compare and Contrast each of the rules for
congruence. Also compare them with the
“non-rules” for congruence.
Can I prove
these triangles
congruent?
MCC9-12.G.SRT.5
Angle-SideAngle (ASA)
Side-AngleSide
(SAS)
Angle-AngleSide
(AAS)
HypotenuseLeg
(HL)
Angle-AngleAngle
(AAA)
Angle-SideSide
(SS)
Two triangles are congruent if and only if corresponding
__________________ and corresponding __________________
are congruent.
Three pairs of
____________________
sides.
You only need ___________ sets of corresponding parts
congruent in order to prove two triangles are congruent.
Do you have the _________________ information?
_
_
_
_
_
_
_
_
_
Two pairs of
_____________________
sides and the
_____________________
angle.
Two pairs of
____________________
angles and the
____________________
side.
Two pairs of
_____________________
sides of a
_____________________
triangle.
Two pairs of
____________________
angles and the
____________________
side.
Triangles may ______
be congruent.
You can ______ prove
___________________.
**You can ____ prove triangle
__________________ or
__________________ with this
postulate (see HL for the only time
this works).
**You ________ prove triangle
____________________________
(AA Similarity Postulate).
_
_
_
_
_
_
_
_
_
_
_
_