Download Section 4.1: Congruent Figures

Warmup
Solve for x in the picture below:
5x-4
3x+22
LEQ: What are congruent figures and their
properties?
Pop Quiz write on your note sheet
Write never, sometimes or always.
1. An acute triangle is ____ congruent to an obtuse triangle.
2. A polygon is ____ congruent to itself.
3. A right triangle is _____ congruent to another right
triangle.
4. If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.
5. If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.
What are congruent polygons?
What are their properties
Talk it over with a partner (no need to write, just
brainstorm)
Slides, flips, and turns
Congruent figures have the same size and shape. When
two figures are congruent, they can be moved so that
they fit exactly on top of each other. Examples of
movements:
Slides
Flips
Turns
Congruent Polygons
 Congruent polygons have congruent corresponding
parts aka matching sides and angles.
 Sides and angles must match up after flipped,
turned, or slid.

Order is critical!!
Name the corresponding sides
and angles
A
B
E
C
<A corresponds to <E
<B corresponds to <F
<C corresponds to <D
D
F
AC corresponds to ED
BC corresponds to FD
AB corresponds to EF
If ABCDE  FGHIJ…
Corresponding angles/sides are congruent. Order
matters in congruency statement.
A
E
B
J
C
D
Ex. <A  <F
<D  <I
CD  HI
F
AE  FJ
I
H
G
Congruent Triangles
3 pairs of congruent angles
3 pairs of congruent sides
A
R
B
G
C
E
Congruency statement: ABC 
EGR
*Applications to Proofs
 When the definition of congruent
triangles is used in a proof we write,
Corr. parts of
Δ’s are 
or CPCTC !!!
Examples of CPCTC
If ΔEFG  ΔRTW, and this is used in a proof before the last
step (meaning we need to use this fact to make other
conclusions), then any conclusions we make based off of
this congruency statement has the reason “corresponding
parts of congruent triangles are congruent or CPCTC”
Closure to 4.1
 Go back to pop quiz
1. An acute triangle is ____ congruent to an obtuse triangle.
2. A polygon is ____ congruent to itself.
3. A right triangle is _____ congruent to another right
triangle.
4. If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.
5. If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.
Hwk: p. 200-202
1-12, 30-35, 38-40