Title: 4.3 Congruent Triangles
14.3 Congruent Triangles
- We will
- name and label corresponding parts of
congruent triangles. - identify congruence transformations.
2Corresponding 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.
3Corresponding 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.
4Corresponding 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
6Example 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.
7Example 3-1c
Answer
8Properties of Triangle Congruence
- Congruence of triangles is reflexive, symmetric,
and transitive. - REFLEXIVE
?JKL ?JKL
K
K
L
L
J
J
9Properties of Triangle Congruence
- Congruence of triangles is reflexive, symmetric,
and transitive. - SYMMETRIC
If ?JKL ?PQR, then ?PQR ?JKL.
K
Q
L
R
J
P
10Properties 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
11IDENTIFY CONGRUENCE TRANSFORMATIONS
If you slide ?ABC down and to the right, it is
still congruent to ?DEF.
B
C
A
12IDENTIFY CONGRUENCE TRANSFORMATIONS
If you turn ?ABC, it is still congruent to ?DEF.
A
B
C
13IDENTIFY CONGRUENCE TRANSFORMATIONS
If you flip ?ABC, it is still congruent to ?DEF.
A
C
B
14Example 3-2a
15Example 3-2b
Use the Distance Formula to find the length of
each side of the triangles.
16Example 3-2b
Use the Distance Formula to find the length of
each side of the triangles.
17Example 3-2b
Use the Distance Formula to find the length of
each side of the triangles.
18Example 3-2c
TempCopy
Use a protractor to measure the angles of the
triangles. You will find that the measures are
the same.
19Example 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.
20Example 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.
21Example 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