Download Activity 11 - Northwest ISD Moodle

CONGRUENCE
TRANSFORMATIONS & TRIANGLE
CONGRUENCE
Unit 5: Activity 11 & 12
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Date Learning Target
10/20 Congruence
10/26 Correspondence
Page
#
60
64
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Learning Task:
I will use corresponding parts of congruent
figures to find unknown angles or side
lengths in the congruent figures.
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
➤ Congruent
Figures - figures in which one maps
to the other by a composition of rigid motions
➤ Congruent
Figures have the same measures
➤ Congruent
Triangles - triangles that have the
same size and shape
➤ Two
triangles are congruent if and only if one
can be obtained from the other by a sequence
of rigid motions
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Establish the correspondence from the congruency statement
B
ΔABC ≅ ΔDEF
A
∠D
∠A ≅ _____
∠E
∠B ≅ _____
∠C ≅ _____
∠F
E
C
D
F
DE
AB ≅ _____
EF
BC ≅ _____
DF
AC ≅ _____
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
ΔEHG ≅ ΔKFG
∠E ≅ _____
∠H ≅ _____
∠EGH ≅ _____
F
E
G
EG ≅ _____
EH ≅ _____
HG ≅ _____
H
K
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
ΔABC ≅ ΔCDA
∠B ≅ _____
∠BAC ≅ _____
∠BCA ≅ _____
B
C
BC ≅ _____
AB ≅ _____
AC ≅ _____
A
D
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Establish the correspondence from the congruent parts
F
C
A
B
E
ΔABC ≅ _____
ΔDEF
D
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
What information about the triangles is
shown in these drawings?
K
D
A
W L
U
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
If ΔDOG ≅ ΔCAT and DO = 10, OG = 12,
DG = 16 and AT = 2x + 6, then x = ?
Establish the correspondence from the congruency statement
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Date Learning Target
10/20 Congruence
10/26 Correspondence
10/27 Triangle Congruence
Page
#
60
64
66
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Learning Task:
I will determine which congruence criteria
can be used to show that two triangles are
congruent.
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Warm-up, Quick Write… p. 66
What would you need to know to draw/construct
a triangle congruent to one drawn by another
student? Explain.
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
SSS
Side Side Side
__________ - _________ - __________
If all 3 pairs of corresponding sides are congruent, then
the two triangles are congruent.
ΔABC ≅ ΔDEF
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
SAS
Side Angle Side
__________ - _________ - __________
If 2 pairs of corresponding sides and the included angle
are congruent, then the two triangles are congruent.
ΔABC ≅ ΔDEF
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
ASA
Angle Side Angle
__________ - _________ - __________
If 2 pairs of corresponding angles and the included side
are congruent, then the two triangles are congruent.
ΔABC ≅ ΔXYZ
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
E
H
F
G
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
P
S
R
Q
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Y
W
X
V
Z
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
K
J
M
L
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Date Learning Target
10/20 Congruence
10/26 Correspondence
10/27 Triangle Congruence
10/28 Proving Triangles Congruent
Page
#
60
64
66
68
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Learning Task:
I will use the congruence criteria to prove
triangles are congurent.
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
AD ≅ AB
DC ≅ BC
Prove:
D
A
ΔADC ≅ ΔABC
C
B
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
AC bisects ∠DAB
∠1 ≅ ∠2
Prove:
D
1
A
ΔABC ≅ ΔADC
2
B
C
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
Prove:
C is the midpoint of
ΔABC ≅ ΔEDC
BC
C is the midpoint of AE
B
E
C
A
D
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
HY ≅ LY
WH / /LF
Prove:
ΔWHY ≅ ΔFLY
H
F
Y
W
L
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Corresponding
Parts of
Congruent
Triangles are
Congruent
If triangles are congruent, or can be
proven to be congruent, then the
corresponding parts would be
congruent.
CPCTC
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
RZ bisects ∠TRS
∠3 ≅ ∠4
Prove:
∠S ≅ ∠T
T
R
1
2
3
Z
4
S
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
Prove:
AB bisects CD
∠A ≅ ∠B
∠C ≅ ∠D
D
A
M
C
B
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
M is the midpoint of AB
∠1 ≅ ∠2
Prove:
∠3 ≅ ∠4
AC ≅ BD
C
A
1
D
3
M
4
2
B
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Warm-up, Quick Write… p. 67
We currently have three criteria to show triangles
are congruent - SSS, SAS, & ASA. It turns out
that two triangles can be congruent if you can
show that two corresponding angles and the NONINCLUDED side are congruent. How is this
possible???
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
➤ Flowchart
Proof - concept map showing a
procedure (proof)
AB ≅ AD
Given
BC ≅ DC
ΔABC ≅ ΔADC
Given
SSS Congruence
AC ≅ AC
Reflexive Property
∠B ≅ ∠D
CPCTC
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
AAS
Angle Angle Side
__________ - _________ - __________
If 2 pairs of corresponding angles and the non-included
side are congruent, then the two triangles are congruent.
ΔABC ≅ ΔDEF
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
M is the midpoint of AB
∠C ≅ ∠D
D
A
M
C
Prove:
ΔAMC ≅ ΔBMD
B
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
HL
Hypotenuse
Leg
____________________ - _________
If the hypotenuse and one leg are congruent in a right
triangle, then the two triangles are congruent.
ΔABC ≅ ΔDEF
CONGRUENCE TRANSFORMATIONS & TRIANGLE CONGRUENCE
Given:
PR ⊥ SQ
SP ≅ QP
S
Prove:
ΔSRP ≅ ΔQRP
P
R
Q