Download Triangle Congruence Notes New.notebook

Triangle Congruence Notes New.notebook
November 28, 2012
Objective: Proving Triangles are Congruent
F
Triangle Congruence!!!
Congruent E
Triangles
J
H
I
G
Congruent Segments
Congruent Angles
Congruency Statement:
Nov 17­9:57 AM
Given:
PLJ≅
Nov 17­9:48 AM
WVB
List all of the congruent sides:
Picture:
Cong. Sides
Cong. Angles
Cong. Tri
List all of the congruent angles:
If PL = 4x + 3, WV = 11 and VB = 15, solve for x.
Nov 17­9:38 AM
Nov 17­9:48 AM
Exit Ticket:
AJB ≅
PQR, solve for x.
Q
A
SSS and SAS
3
19
5x +
If
B
18
R
17
P
J
Nov 17­9:48 AM
Nov 17­2:32 PM
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Triangle Congruence Notes New.notebook
November 28, 2012
If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
F
B
D
SSS
J
H
L
SAS
Side­Angle­Side
Side­Side­Side
I
A
E
C
K
G
ABC ≅ __________ by ________
HIG ≅ __________ by ________
Nov 17­9:48 AM
Nov 17­9:48 AM
Practice: Write a congruency statement and tell why the triangles are congruent.
O
R
L
A
Given: BA≅BD, BA≅BD
Prove:
ABE≅ DBC
B
E
RGL ≅ _______ by ______
G
C
Statements
D
Reasons
Y
B
1.
1.
R
V
2.
CRV ≅ _______ by ______
3.
2. Vertical Angles Thrm.
ABE ≅
DBC
3.
P
C
W
Y
HBY ≅ _______ by ______
B
P
H
Nov 17­9:48 AM
A
Given: B is the midpoint of DC.
AB DC
Prove:
ABD ≅
Nov 30­12:36 PM
ABC
D
B
Reasons
Statements
1.
1. B is the midpoint of DC
2.
2. Definition of a midpoint
3.
3. Given
4.
ABD and
5.
ABD ≅
ABC are right angles.
ABC
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#28-31
4.
5.
6. Reflexive property of ≅
6.
7.
C
ABD ≅
ABC
7.
Nov 15­9:43 AM
Nov 15­9:53 AM
2
Triangle Congruence Notes New.notebook
November 28, 2012
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.
P
N
ASA, AAS, and HL
ASA
R
Angle­Side­Angle
M
O
Q
Nov 17­2:32 PM
Nov 17­9:48 AM
If two angles and a non­included side of a triangle are congruent to the corresponding angles and non­included side of another triangle, then the triangles are congruent.
W
T
AAS
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
HL
Z
C
B
Hypotenuse­Leg
Angle­Angle­Side
S
X
V
U
A
Y
Nov 17­9:48 AM
Nov 17­9:48 AM
What additional information is needed to prove the triangles are congruent by SSS?
Matching
_____SSS
B.
A.
_____SAS
G
W
R
D
C.
_____AAS
_____ASA
D
D.
E.
_____HL
Nov 17­9:48 AM
Nov 17­9:48 AM
3
Triangle Congruence Notes New.notebook
What additional information is needed to prove the triangle FRW is congruent to triangle BMQ by SAS?
F
What additional information is needed to prove trianlge TRY is congruent to triangle IUY by ASA?
R
M
Q
R
November 28, 2012
W
Nov 17­9:48 AM
T
Y
U
I
B
Nov 17­9:48 AM
4