Section 4.2 Apply Congruence and Triangles
Goal  Identify congruent figures.
Congruent figures
All the parts of one figure are congruent to the corresponding parts of the other figure.
(This means that the corresponding sides and corresponding angles are all congruent)
A
O
CAT  DOG
C
T
Corresponding Angles: C D
Corresponding Sides: CA  DO
D
G
A O T G
AT  OG
CT  DG
*When writing congruence statements, make sure you ALWAYS list the corresponding
vertices in the same order*
Example 1: Write a congruence statement for the triangles. Identify all pairs of congruent
corresponding parts.
a.
Angles
Sides
Example 2: In the diagram, ABCDE  FGHIJ. Find the value of x & y.
Checkpoint: In Exercises 1 and 2, use the diagram shown in which FGHJ  STUV.
1. Identify all pairs of congruent corresponding parts.
(2x – 7)°
2. Find the value of x and find mG.
Section 4.2 Apply Congruence and Triangles
Third Angles Theorem
If two angles of one triangle are congruent to two angles of
another triangle, then the third angles are also CONGRUENT.
Example 3:
a. Find mF
b. Find mD
THEOREM 4.4: PROPERTIES OF CONGRUENT TRIANGLES
Reflexive Property of
Congruent Triangles
Symmetric Property of
Congruent Triangles
For any triangle ABC,
ABC  _______
If ABC  DEF,
then ________________.
Sides of Triangles
AB  _______
Sides of Triangles
AB  DE, then DE  _____
Angles of Triangles
A  _______
Angles of Triangles
A  D, then D  ____
Transitive Property of
Congruent Triangles
If ABC  DEF, and DEF 
JKL, then _________________.
Angles of Triangles
A  D and D  J, then
___________________________
Example 4: Write a proof.
Given: FH  JH , FG  JG , FHG  JHG, FGH  JGH
Prove: FGH  JGH
Statements
Reasons
Section 4.2 Apply Congruence and Triangles