Chapter 4: Congruent
Triangles
Lesson 3: Congruent Triangles
Definition of Congruent
Triangles
 Congruent triangles are triangles with
exactly the same size and shape
 CPCTC: Corresponding Parts of
Congruent Triangles are Congruent
 Two triangles are congruent if and only if
their corresponding parts are congruent
Corresponding Parts
A
 Corresponding
parts have the
same congruence
markings

B
C
H
I
J
 AB  HI
 AC  HJ
 BC  IJ
 A   H
 B   I
 C   J
Congruence Transformations
 Slide or Translation: the triangle is
in the same position farther down,
up, or across the page
 Turn or Rotation: the triangle is
spun around a point (usually one of
the angles)
 Flip or reflection: the triangle is
shown in a mirror image across a line
of symmetry
Write a congruence
statement for the
triangles.
Name the
corresponding
congruent angles
and the
corresponding
congruent sides for
triangles.
In the diagram, ΔITP  ΔNGO. Find the values of
x and y.
In the diagram, ΔFHJ  ΔHFG. Find the values of
x and y.
Find the missing information in the following proof.
Prove: ΔQNP  ΔOPN
Proof:
1. Given
2. Reflexive Property of
2.
Congruence
3. Q  O, NPQ  PNO 3. Given
4. _________________
4. QNP  ONP
?
1.
5. ΔQNP  ΔOPN
5. Definition of Congruent
Polygons
Write a two-column proof.
Prove: ΔLMN  ΔPON