Download 4.3 Congruent Triangles

4.3 Congruent Triangles
Then: You identified and used congruent angles.
Now: 1. Name and use corresponding parts of
congruent triangles.
2. Prove triangles congruent using the definition
of congruence.
4.3 Congruent Triangles
Corresponding parts-
BCA  EFD
Corresponding angles:
Corresponding sides:
http://www.tutornext.com/system/files/u19/Congruent_triangles.gif
Example 1:
a. Identify all pairs of congruent corresponding parts.
Write another congruence statement for the
triangles.
 JKL  NKM
Corresponding angles:
___  ___
___  ___
___  ___
Example 1 cont.
Corresponding Sides:
_____  _____
_____  _____
_____  _____
Congruence statement: ______  ______
Example 1:
Write a congruence statement for any figures that can
be proved congruent. Explain your reasoning.
b.
c.
_________________
______________
Example 2:
In the diagram, ABC  DEF
a. Find the value of x.
b. Find the value of y.
Example 2:
In the diagram, ΔFHJ  ΔHFG.
c. Find the value of x.
d. Find the value of y.
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 are congruent.
http://www.wyzant.com/Help/Images/congruent2.gif
Example 3:
a. TILES
A drawing of a tile contains a series of triangles,
rectangles, squares, and a circle.
If ΔKLM  ΔNJL, KLM  KML, and mKML = 47.5,
find mLNJ.
Example 3:
Find the value of y.
b.
c.
Example 4: Prove that triangles are congruent.
a. Given: FH  JH, FG  JG, FHG  JHG,
FGH  JGH
Prove: FGH  JGH
Statements
1. FH  JH, FG  JG
2. HG  HG
3. FHG  JHG,
FGH  JGH
4. HFG   HJG
5. FGH  JGH
Reasons
1. _________________
2. _________________
3. _________________
4. __________________
5. __________________
Theorem 4.4- Properties of Triangle Congruence
Reflexive Property of Triangle Congruence:
ABC  ABC.
Symmetric Property of Triangle Congruence :
If ABC  DEF, then DEF  ABC.
Transitive Property of Triangle Congruence :
If ABC  DEF and DEF  JKL,
then ABC  JKL.
Example 4:
b. In the diagram, E is the midpoint of AC and BD.
Show that ABE  CDE.
4.2 Assignment:
p. 259-263 #10,11, 13-16, 18-20, 23, 24, 28,
30, 34, 35, 37, 43-46, 48-50,
55-57
#23 and 24 proofs on handout