Congruent Triangles

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Lesson 4-3

• Congruent Triangles

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Transparency 4-3
5-Minute Check on Lesson 4-2
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
C
D
111?
115?
A
B
65?
69?
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Transparency 4-3
5-Minute Check on Lesson 4-2
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
C
D
111?
115?
A
B
65?
69?
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Objectives

• Name and label corresponding parts of congruent
  triangles
• Identify congruence transformations

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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)

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Properties of Triangle Congruence

• Reflexive ?JKL ? ? JKL
• Symmetric if ? JKL ? ? PQR, then ? PQR ? ? JKL
• Transitive if ? JKL ? ? PQR and ? PQR ? ? XYZ,
  then ? JKL ? ? XYZ

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Congruent Triangles
X
A
C
Y
B
Z
The vertices of the two triangles correspond in
the same order as the letters naming the
triangle
?ABC ? ?XYZ ?A ? ?X ?B ? ?Y ?C ? ?Z AB ?
XY BC ? YZ CA ? ZX CPCTC Corresponding Parts of
Congruent Triangles are Congruent
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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.
Name the congruent triangles.
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Answer

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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.
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Use the Distance Formula to find the length of
each side of the triangles.
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Use a protractor to measure the angles of the
triangles. You will find that the measures are
the same.
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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.

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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.
b. Name the congruence transformation for ?ABC
and ?A?B?C?.
Answer turn
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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