Transcript Congruence and Triangles

Congruent
Triangles
Chapter 4-3
Standard 5.0 Students prove that triangles are
congruent or similar, and they are able to use the
concept of corresponding parts of congruent
triangles.
Congruent Triangles
• Two triangles are congruent if all of
their corresponding sides and
corresponding angles are congruent.
Y
Congruent Triangles
B
ABC  YXZ
C
A
Congruent Angles
A  Y
X
Order is
important!!!
Congruent Sides
AB  YX
B  X
BC  XZ
C  Z
AC  YZ
Z
Corresponding Congruent Parts
B. ARCHITECTURE A tower's roof
is composed of congruent
triangles all converging toward a
point at the top. Name the
congruent triangles.
Answer: ΔHIJ  ΔKIL
Corresponding Congruent Parts
A. ARCHITECTURE A tower's roof
is composed of congruent
triangles all converging toward a
point at the top. Name the
corresponding congruent angles
and sides of
A. The support beams on the fence form congruent
triangles. Which of the following congruence
statements directly matches corresponding angles or
sides ΔABC and ΔDEF?
A.
B.
C.
D.
B. The support beams on the fence form congruent
triangles. Which statement correctly names the
congruent triangles?
A. ΔACB  ΔEDF
B. ΔCBA  ΔFED
C. ΔBCA  ΔDFE
D. ΔBAC  ΔEFD
B
Third Angles Theorem
C
E
F
A
• If two angles of one triangle are congruent
to two angles of another triangle, then the
third angles are also congruent.
If A  D and B  E, then C  F.
D
 Congruence Properties
• Reflexive Property of  
Every triangle is congruent to itself
• Symmetric Property of  
If ABC  DEF, then DEF  ABC.
• Transitive Property of  
If ABC  DEF, and DEF  JKL,
then
ABC  JKL.
Transformations in the Coordinate Plane
A. COORDINATE GEOMETRY The vertices of
are R(─3, 0), S(0, 5), and T(1, 1). The vertices of
ST are R(3, 0), S(0, ─5), and T(─1, ─1).
Use the Distance Formula to find
the length of each side of the
triangles.
Transformations in the Coordinate Plane
Transformations in the Coordinate Plane
Homework
Chapter 4-3
• Pg 220:
6-9
10-13 use the distance
formula to show that the
sides are congruent
20, 25-28, 39-41