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GEOMETRY: Chapter 4
4.2: Congruence and Triangles
In two congruent figures, all the parts
of one figure are congruent to the
corresponding parts of the other
figure.
In congruent polygons, this means that
the corresponding angles and the
corresponding sides are congruent.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 225.
Congruence Statements
To express that two figures are congruent,
use the congruent symbol,  , and list
the corresponding vertices in the same
order.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 225.
Ex. 1. Write a congruence statement for the
triangles shown. Identify all pairs of
congruent corresponding parts.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 226.
Ex. 1. Write a congruence statement for the
triangles shown. Identify all pairs of
congruent corresponding parts.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 226.
Ex. 2. In the diagram, ABCD  FGHK.
a. Find the value of x. (5)
b. Find the value of y. (12)
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 226.
Ex. 3: Maggie took the piece of fabric STUV
shown in the diagram and cut it on the
diagonal to make a scarf for her and a
friend. Are the two pieces the same size and
shape? Explain.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.
Theorem 4.3: Third Angles Theorem
If two angles of one triangle are congruent to
two angles of another triangle, then the third
angles are also congruent.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.
Ex. 4: Find m  YXW.
1050
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.
Ex. 5
Given: SV  RV , TV  WV , ST  RW , T  W
Prove: STV  RWV
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.
Theorem 4.4: Properties of Congruent Triangles
Reflexive Property of Congruent Triangles
For any triangle ABC, ABC  ABC
Symmetric Property of Congruent Triangles
If ABC  DEF , then DEF  ABC.
Transitive Property of Congruent Triangles
If
ABC  DEF and DEF  JKL, then
ABC  JKL.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 228.