4.3 Congruent Triangles

1
4.3 Congruent Triangles

• We will
• name and label corresponding parts of
  congruent triangles.
• identify congruence transformations.

2
Corresponding parts of congruent triangles

• Triangles that are the same size and shape are
  congruent triangles.
• Each triangle has three angles and three sides.
  If all six corresponding parts are congruent,
  then the triangles are congruent.

3
Corresponding parts of congruent triangles
If ?ABC is congruent to ?XYZ , then vertices of
the two triangles correspond in the same order as
the letter naming the triangles.
4
Corresponding parts of congruent triangles
This correspondence of vertices can be used to
name the corresponding congruent sides and angles
of the two triangles.
5

• Definition of Congruent Triangles (CPCTC)
• Two triangles are congruent if and only if their
  corresponding parts
• are congruent.
• CPCTC
• Corresponding Parts of Congruent Triangles are
  Congruent

6
Example 3-1a
ARCHITECTURE A tower roof is composed of
congruent triangles all converging toward a
point at the top. Name the corresponding
congruent angles and sides of ?HIJ and ?LIK.
7
Example 3-1c
Answer

8
Properties of Triangle Congruence

• Congruence of triangles is reflexive, symmetric,
  and transitive.
• REFLEXIVE

?JKL ?JKL
K
K

L
L
J
J
9
Properties of Triangle Congruence

• Congruence of triangles is reflexive, symmetric,
  and transitive.
• SYMMETRIC

If ?JKL ?PQR, then ?PQR ?JKL.
K
Q
L

R
J
P
10
Properties of Triangle Congruence

• Congruence of triangles is reflexive, symmetric,
  and transitive.
• TRANSITIVE

If ?JKL ?PQR, and ?PQR ?XYZ, then ?JKL
?XYZ.

K
Q

L
R
J
Y
P
Z
X
11
IDENTIFY CONGRUENCE TRANSFORMATIONS
If you slide ?ABC down and to the right, it is
still congruent to ?DEF.
B
C
A
12
IDENTIFY CONGRUENCE TRANSFORMATIONS
If you turn ?ABC, it is still congruent to ?DEF.
A
B
C
13
IDENTIFY CONGRUENCE TRANSFORMATIONS
If you flip ?ABC, it is still congruent to ?DEF.
A
C
B
14
Example 3-2a
15
Example 3-2b
Use the Distance Formula to find the length of
each side of the triangles.
16
Example 3-2b
Use the Distance Formula to find the length of
each side of the triangles.
17
Example 3-2b
Use the Distance Formula to find the length of
each side of the triangles.
18
Example 3-2c
TempCopy
Use a protractor to measure the angles of the
triangles. You will find that the measures are
the same.
19
Example 3-2d
COORDINATE GEOMETRY The vertices of ?RST are
R(-3, 0), S(0, 5), and T(1, 1). The vertices of
?R?S?T ? are R?(3, 0), S?(0, -5), and T?(-1, -1).
Name the congruence transformation for ?RST and
?R?S?T?.
Answer ?R?S?T? is a turn of ?RST.

20
Example 3-2f
COORDINATE GEOMETRY The vertices of ?ABC are
A(5, 5), B(0, 3), and C(4, 1). The vertices of
?A?B?C? are A?(5, 5), B?(0, 3), and C?(4, 1).
Answer

Use a protractor to verify that corresponding
angles are congruent.
21
Example 3-2g
b. Name the congruence transformation for ?ABC
and ?A?B?C?.
Answer turn

22

• BOOKWORK
• p. 195 9 19,
• 22 25 (just name the congruence
  transformation)
• HOMEWORK
• p.198 Practice Quiz