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Name: _____________________________
Geometry
Chapter 4.3: Congruent Triangles
We learned about congruent angles in chapter 4.2 and we will now work on applying congruence of angles and
sides to proving that certain triangles are congruent to each other.
Key Concept: Definition of Congruent Polygons
Two polygons are congruent if and only if their
corresponding parts are congruent
Corresponding Angles:
Corresponding Sides:
Congruent Statement:
Valid congruence statements for congruent polygons
list corresponding vertices in the same order.
Theorem 4.3: Third Angles Theorem
If two angles of one triangle are congruent to two
angles of a second triangle, then the third angles of
the triangles are congruent.
Theorem 4.4: Properties of Triangle Congruence
Reflexive Property of Triangle Congruence
Symmetric Property of Triangle Congruence
Transitive Property of Triangle Congruence
Examples:
1) Identify each congruent part then write a congruence statement for the
triangles:
Name: _____________________________
Geometry
Chapter 4.3: Congruent Triangles
2) Polygon ABCD is congruent to polygon PQRS.
Find x and y
3) Draw and label a figure with the following criteria. Then find the values of x and y.
ABC  DEF , AB  7 , BC  9 , AC  11  x , DE  2 y  5
4) Write a two column proof.
Given: P  R ,
PSQ  RSQ ,
PQ  RQ , PS  RS
Prove: PQS  RQS
Statements
Reasons