Transcript Lesson 4.1 Congruent Figures

Jay:
You
know
the
difference
between
you and me? I make this look GOOD.
4.1
Congruent Figures
Congruent Polygons
Have the same size and shape.
You can slide, flip, or turn the figure so that it fits
exactly on the other one.
You can determine whether two figures are congruent
by comparing their corresponding parts.
Order is very important!
When you name congruent polygons, you must list
corresponding parts in the same order.
4.1
Example 1
B
F
A
E
D
C
ABCD
G
H
EFGH
Complete each congruence statement.
AB
_____
EF
A
_____
E
BC
_____
FG
B
_____
F
CD
_____
GH
C
_____
G
DA
_____
HE
D
_____
H
4.1
Example 2
Suppose that ΔWYS ΔMKV. If m W=62 and m Y=35,
what is m V? Explain.
Y
K
35°
W
62°
S
62 + 35 + m S = 180
m S = 83
m S = m V = 83
V
M
Triangle Angle-Sum Thm.
Subtraction
4.1
Example 2
Suppose that ΔWYS ΔMKV. If m W=62 and m Y=35,
what is m V? Explain.
Y
K
35°
W
62°
S
W
M
Y
S
K
V
V
M
Corresponding parts of
congruent triangles are
congruent. (CPCTC)
4.1
Congruent Figures
How many conditions must be proved to show that
two triangles are congruent?
The definition states that the figures must have
congruent sides and angles.
Since there are 3 sides and 3 angles in a triangle, we
will need 6 congruence statements to prove two
triangles congruent.
4.1
Example 3
D
Is Δ ABD
Δ CBD?
A
AD
DC
Given
BD
BD
Reflexive Prop of
B
C
Is this enough to conclude the triangles are congruent?
NO.
4.1
Congruent Figures
Theorem 4.1 Third Angles Theorem
If two angles of one triangle are congruent to two
angles of another triangle, then the third angles are
congruent.
D
A
B
If  A
C
 D and  B
E
F
 E, Then  C  F
Note: This is the reason why we cannot use AAA to prove triangles congruent.
Proof p. 220
4.1
Example 4
Given:  A
 D, AE
Prove: Δ AEB
DC, EB
CB, BA
BD
Δ DCB
A
B
C
D
E
A
 D, AE
DC, EB
CB, BA
BD
Given
 ABE
 DBC
Vertical angles are
 AEB
 DCB
Δ AEB
Δ DCB
Third Angle Thm.
Def. of
Δ’s
Homework
• pg. 222 #10-29
12
Iextraordinary
need to believe,
that
something
is possible.
There
has
to
be
a
mathematical
explanation for how bad that tie is