Transcript Chapter 4.2 Notes: Apply Congruence and Triangles

Chapter 4.2 Notes: Apply
Congruence and Triangles
Goal: You will identify congruent figures.
• Two geometric figures are congruent if they have
exactly the same size and shape.
Congruence Statements
• 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 sides and the corresponding angles
are congruent.
• When you write a congruence statement for two
polygons, always list the corresponding vertices in
the same order.
Congruence Statement: __________________
Corresponding angles: ___________________
Corresponding sides: ____________________
Ex.1: Write a congruence statement for the triangles.
Identify all pairs of congruent corresponding parts.
Ex.2: In the diagram, DEFG  SPQR .
a. Find the value of x.
b. Find the value of y.
Ex.3: In the diagram below, ABGH  CDEF .
a. Identify all pairs of congruent corresponding
parts.
b. Find the value of x and find mH .
Ex.4: Show that PTS  RTQ.
• 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.
Ex.5: Find mBDC .
Ex.6: In the diagram, what is mDCN ?
Ex.7: The two triangles are congruent. Identify all
angles and sides that are congruent. Then write a
congruence statement.
Ex.8: In the diagram, ABCD  FGHK .
a. Find the value of x.
b. Find the value of y.
Properties of Congruent Triangles
• 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 & DEF  JKL , then
ABC  JKL .