Transcript Section 3.1 What Are Congruent Figures?

Section 3.1
What Are Congruent Figures?
Congruent Figures
A non-geometry student may describe
CONGRUENT triangles as having the same
size and shape
D
A
 A geometry
student would
describe them as having
6 pairs of corresponding
congruent
parts:
B
F

◦
◦
congruent angles
congruent segments
C
E
AB  DF AC  DE BC  FE
A  D B  F C  E
And therefore…
ABC  DFE
Congruent Triangles

Congruent triangles

If all pairs of corresponding parts are
S
congruent, then
X
R
XYZ  TRS
Y
Z
T
X  T Y  R Z  S
XY  TR YZ  RS XZ  TS
Vocabulary

Congruent Polygons

All pairs of corresponding parts (angles and sides) are
congruent.
P
A
Q
D
B
R
C
S
A  P, B  Q, C  R, D  S
AB  PQ, BC  QR, CD  RS , and DA  SP
Parallelogram ABCD

Parallelogram PQRS
Caution

ABC  XYZ
Be careful when naming
congruent figures,
C
corresponding parts must
be listed in the same order

Y
To check this, match up
the vertices of the
corresponding angles.
Z
X
This notation means that
BAC  YXZ
ABC  XYZ
BCA  YZX
B
A
and
AB  XY
BC  YZ
CA  ZX
Caution


Sometimes it is
difficult to tell what
parts of a congruent
figure are congruent.
To keep from making
mistakes:


Label your congruent
sides and angles with
tick marks
and/or
Use colored pencils
ABC  XYZ
C
Y
X
B
A
Z
Reflexive Property

Reflexive Property
(Postulate)
F

Any figure or segment
is congruent to itself
Given the diagram as shown, what else
do you need to know in order to say that
 FGH  
G
H
I
FIH ?
FH  FH
What property could we use to show this is true?
The reflexive property, it says that any
figure or segment is congruent to itself.
Based on the markings on these triangles, NAME
the congruent triangles correctly.
O
P
3
K
B
H
A
T
4
LM
Y
N
OKL  PMN
MAT  HTA
C
V
A
M
W
X
D
BAD  BCD
WVY  WXZ
Z
Hints for finding congruent parts…
Try and find out if
your triangles are
Reflections or Flips
Translations or Slides
Rotations or Turns
Reflection (or Flip)
A figure has been reflected if it has been
flipped over a line.
B
E
AB  DE AC  DF BC  EF
D
A
A  D B  E C  F
ABC  DEF
C
F
Translation (or Slide)

The two figures shown are congruent.
The correspondence is evident if we slide
or translate one onto the other.
O
P
S
L
LM  PQ LO  PS ON  SR MN  QR
L  P M  Q N  R O  S
M
N
Q
LMNO  PQRS
R
Rotation (or turn)

A figure that has been rotated has been turned
to form a congruent figure. Sometimes it is
easier to see the corresponding parts if we rotate
one onto the other.
F
FL  KL FG  KJ GL  JL
K
L  L F  K G  J
J
G
L
KLJ  FLG
K
J
Each pair of triangles is CONGRUENT. Do they
1
show a Reflection, Translation
, or Rotation?
2
3
1
reflection
4
5
translation
9
8
rotation
reflection
11
7
6
12
10
translation
reflection
REMEMBER…by definition…
Corresponding
Parts of
Congruent
Triangles are
Congruent