Download G Notes 4.6 and 4.7 Congruence in Right and Overlapping

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4.6 & 4.7 Congruence in
Right Triangles &
Overlapping Triangles
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WS 4.6 & 4.7
Hypotenuse-Leg Theorem :
If a hypotenuse and a leg of one right triangle
are congruent to the hypotenuse and a leg of
another right triangle then the triangles are
congruent.
X
Y
M
Z
L
N
E1
Given : PS  PT,
and PRS  PRT
Prove : PRS  PRT
P
S
Statement
PRS  PRT
PRS  PRT are
right angles.
Reason
given
linear pair
PRS & PRT
are right
's.
def of right triangles
PS  PT
PR  PR
given
reflexive
Hypotenuse  Leg
PRS  PRT
R
T
What additional information would prove each pair of
triangles congruent by Hypotenuse-Leg Theorem?
E2 M
E3
Q
Z
X
D
K
N
O
R
T
P
mZ  mT  90
MO  QR
For what values of x or y are the triangles congruent by
Hypotenuse-Leg Theorem?
X
Z 2y-10
E4
D
K
T
2 y  10  90
y  50
F
A
E5
15
B
3x+7
C
E
15  3x  7
8 x
3
D
CPCTC: Corresponding Parts of Congruent Triangles
are Congruent.
X
Y
M
Z
L
N
Separate and redraw the overlapping triangles.
Identify the common triangles and angles or sides.
E1
X
E2
E
Z
V
B
C
A
E
E
Y
X
Z
Z
B
A
A
AE  AE
V
V
C
ZV  ZV
Y
Separate and redraw the overlapping triangles.
Identify the common triangles and angles or sides.
E3
E4
X
D
A
V
E
Z
U
W
B
X
C
Y
A
BC  BC
X
Z
V
D
W
B
X   X
C
B
C
Y
E5
Given : CA  CE ,
C
and BA  DE
Prove : BXA  DXE
Statement
1) BA  DE
2) CA  CE
B
X
A
Reason
1) given
2) given
3)CAE  CEA 3) Isosceles triangletheroem
4) AE  AE
4) reflexive
5) BAE  DEA
6) ABE  EDA
5) SAS
7) BXA  DXE
7) vertical
8) BXA  DXE
8) AAS
6) CPCTC
D
E