Transcript Lesson 1 Contents

Lesson 4-3
Congruent Triangles
5-Minute Check on Lesson 4-2
Transparency 4-3
Find the measure of each angle.
1. m1
2. m2
3. m3
4. m4
5. m5
6.
Two angles of a triangle measure 46 and 65.
What is the measure of the third angle?
Standardized Test Practice:
A
65
B
69
C
111
D
115
5-Minute Check on Lesson 4-2
Transparency 4-3
Find the measure of each angle.
1. m1
115
2. m2
72
3. m3
57
4. m4
18
5. m5
122
6.
Two angles of a triangle measure 46 and 65.
What is the measure of the third angle?
Standardized Test Practice:
A
65
B
69
C
111
D
115
Objectives
• Name and label corresponding parts of
congruent triangles
• Identify congruence transformations
Vocabulary
• Congruent triangles – have the same size and
shape (corresponding angles and sides )
• Congruence Transformations:
– Slide (also known as a translation)
– Turn (also known as a rotation)
– Flip (also known as a reflection)
Properties of Triangle Congruence
•
Reflexive – ∆JKL  ∆ JKL
•
Symmetric – if ∆ JKL  ∆ PQR, then ∆ PQR 
∆ JKL
•
Transitive – if ∆ JKL  ∆ PQR and ∆ PQR  ∆
XYZ, then ∆ JKL  ∆ XYZ
Congruent Triangles
A
X
C
Y
B
The vertices of the two triangles correspond in the same order as the letters
naming the triangle
▲ABC  ▲XYZ
A  X
AB  XY
B  Y
BC  YZ
C  Z
CA  ZX
CPCTC – Corresponding Parts of Congruent Triangles are Congruent
Z
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.
Answer: Since corresponding parts of congruent triangles
are congruent,
Name the congruent triangles.
Answer: HIJ LIK
The support beams on the fence form congruent
triangles.
a. Name the corresponding
congruent angles and sides of
ABC and DEF.
Answer:
b. Name the congruent triangles.
Answer: ABC DEF
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).
Verify that RST  RST.
Use the Distance Formula to find the
length of each side of the triangles.
Use the Distance Formula to find the length of each side of
the triangles.
Answer: The lengths of the corresponding sides of two
triangles are equal. Therefore, by the definition
of congruence,
Use a protractor to measure the angles of the triangles. You
will find that the measures are the same.
In conclusion, because
,
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.
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).
a. Verify that ABC ABC.
Answer:
Use a protractor to verify that
corresponding angles are
congruent.
b. Name the congruence transformation for ABC and ABC.
Answer: turn
Summary & Homework
• Summary:
– Two triangles are congruent when all of
their corresponding parts are congruent.
– Order is important!
• Homework:
– pg 195-198: 9-12, 22-25, 40-42