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Geometry Lesson 4-2 Day 1: Apply Congruence and Triangles H.W. 1-14,36-40
Congruent figures: _________________________________________________________________________
Corresponding parts: ________________________________________________________________________
Example 1: Write a congruence statement for the triangles. Identify all pairs of congruent corresponding
parts.
Example 2: In the diagram, QRST  WXYZ.
a.) Find the value of x.
b.) Find the value of y.
Example 3: If you cut the map in half along PR , will the sections of the map be the same size and shape?
Explain.
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 _______________.
Example 4: Find mV.
Example 5:
Given: FH  JH , FG  JG
FHG  JHG, FGH  JGH
Prove: FGH  JGH
Statements
1. FH  JH , FG  JG
2. ___________
Reasons
1. __________________________________________
3. FHG  JHG,
FGH  JGH
3. __________________________________________
4. __________
4. Third Angles Theorem
5. FGH  JGH
5. _________________________________________
2. Reflexive Property of Congruence
THEOREM 4.4: PROPERTIES OF CONGRUENT TRIANGLES
Reflexive Property of Congruent Triangles
For any triangle ABC, ABC  _________.
Symmetric Property of Congruent Triangles
If ABC  DEF, then ________________
Transitive Property of Congruent Triangles
If ABC  DEF, and
DEF  JKL, then _________________.
Example 6: In the diagram at the right, E is the midpoint of AC and BD . Show that ABE  CDE.