Download Notes 5A Congruence and Triangles.notebook

Notes 5A Congruence and Triangles.notebook
October 31, 2011
Bell work
Graph the equation 3x + 2y = ­2
Notes 5A: Congruence and Triangles
Goal: Identify congruent figures and corresponding parts.
Vocabulary:
When two geometric figures are congruent, there is a correspondence
between their angles and sides such that corresponding angles are
congruent and corresponding sides are congruent
1. Given that
CAT
DOG, name three pairs of congruent sides.
C
D
A
T
2. Given
ABC
O
G
XYZ, name three pairs of congruent angles
Y
B
A
X
C
Z
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Notes 5A Congruence and Triangles.notebook
In the diagram,
A
ABC
October 31, 2011
DEF, Complete the statement.
D
80
8cm
C
35
B
F
1. <C
______
2. BC
_______
E
5. AC=______
6.
FDE ______
3. m<A= ______
4. m<F= _______
There are 5 ways to prove triangles are congruent.
1. Postulate 19: side-side-side (sss)
if three sides of one trianlge are congruent to three sides of a
second triangle, then they are congruent.
Draw an example:
2. Postulate 20: side-angle-side (sas)
If two sides and the included angle (the angle must be
between the ~
= sides) of one triangle are congruent to two
sides and the included angle of a second triangle, then the
two triangles are congruent.
Draw an example:
2
Notes 5A Congruence and Triangles.notebook
October 31, 2011
3. Postulate 21: angle-side-angle (asa)
If two angles and the included side (side must be between the
two ~
= angles) of one triangle are congruent to two angles and
the included side of a second triangle, then the two triangles
are congruent.
Draw an example:
4. Theorem 4.5: angle-angle-side (aas)
If two angles and a non-included side (the side is not between the 2
~
= angles) of one triangle are congruent to two angles and the
corresponding nonincluded side of a second triangle, then the two
triangles are congruent.
Draw an example:
5. Hypotenuse-leg (HL) congruence theorem
If the hypotenuse and leg of a right triangle are congruent to
the hypotenuse and leg of a second triangle, then the two
triangles are congruent.
Draw an example:
3
Notes 5A Congruence and Triangles.notebook
October 31, 2011
example: proving triangles are congruent
1.
2.
3.
(
(
5.
4.
Complete the statement.
~
=
ABC, then XY
~
= _____
1. If
XYZ
2. If
BAT ~
=
DOG, then <T
~
= _____
3. If
SAP
~
=
MET, then PS
~
= _____
4. If
GHI
~
=
PQR, then IH
~
= _____
5. If
RUN
~
=
BAT, then
6. If
PMN
~
=
CRS, then <M ~
= _____
NRU
~
= _____
4
Notes 5A Congruence and Triangles.notebook
October 31, 2011
Identify any figures that can be proved congruent. Explain your reasoning.
For those that can be proved congruent, write a congruence statement.
)
E
P
)
G
N
2.
F
T
)
)
)
)
Q
)
D
)
1.
M
R
NOT
Possible
3.
X
(
Y
W
(
Z
Find the value of x and y.
B
ABC
A
DEF
F
C
22
~
=
3x
9
(5y-3)
E
D
5
Notes 5A Congruence and Triangles.notebook
October 31, 2011
Assignment Worksheet 5A
6