Download Geometry 4-3 Congruent Triangles 10-29

11/6/2015
Five-Minute Check (over Lesson 4–2)
CCSS
Then/Now
New Vocabulary
Key Concept: Definition of Congruent Polygons
Example 1: Identify Corresponding Congruent Parts
Example 2: Use Corresponding Parts of Congruent Triangles
Theorem 4.3: Third Angles Theorem
Example 3: Real-World Example: Use the Third Angles
Theorem
Example 4: Prove that Two Triangles are Congruent
Theorem 4.4: Properties of Triangle Congruence
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Over Lesson 4–2
Find m∠
∠1.
Find m∠
∠2.
Find m∠
∠3.
Find m∠
∠4.
Find m∠
∠5.
One angle in an isosceles triangle has a measure of
80°. What is the measure of one of the other two
angles?
Over Lesson 4–2
Find m∠
∠1.
A. 115
B. 105
C. 75
D. 65
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Over Lesson 4–2
Find m∠
∠2.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m∠
∠3.
A. 75
B. 72
C. 57
D. 40
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Over Lesson 4–2
Find m∠
∠4.
A. 18
B. 28
C. 50
D. 75
Over Lesson 4–2
Find m∠
∠5.
A. 70
B. 90
C. 122
D. 140
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Over Lesson 4–2
One angle in an isosceles triangle has a measure of
80°. What is the measure of one of the other two
angles?
A. 35
B. 40
C. 50
D. 100
Content Standards
G.CO.7 Use the definition of congruence in terms of
rigid motions to show that two triangles are
congruent if and only if corresponding pairs of sides
and corresponding pairs of angles are congruent.
G.SRT.5 Use congruence and similarity criteria for
triangles to solve problems and to prove
relationships in geometric figures.
Mathematical Practices
6 Attend to precision.
3 Construct viable arguments and critique the
reasoning of others.
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You identified and used congruent angles.
• Name and use corresponding parts of
congruent polygons.
• Prove triangles congruent using the
definition of congruence.
• congruent
• congruent polygons
• corresponding parts
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Identify Corresponding Congruent Parts
The polygons are congruent.
Identify all of the congruent
corresponding parts. Then
write a congruence
statement.
Angles:∠ ≅ ∠, ∠ ≅ ∠, ∠ ≅ ∠,
∠
≅ ∠, ∠ ≅ ∠
Sides: ≅ , ≅ , ≅ ,
≅ , ≅ Answer: ABCDE ≅ RTPSQ.
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The support beams on the fence form congruent
triangles. In the figure ∆ABC ≅ ∆DEF, which of the
following congruence statements correctly
identifies corresponding angles or sides?
A.
B.
C.
D.
Use Corresponding Parts of Congruent Triangles
In the diagram, ∆ITP ≅ ∆NGO. Find the values of
x and y.
∠O
m∠O
6y – 14
6y
y
≅
=
=
=
=
∠P
m∠P
40
54
9
Answer: x = 25.5, y = 9
NG
x – 2y
x – 2(9)
x – 18
x
=
=
=
=
=
IT
7.5
7.5
7.5
25.5
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In the diagram, ∆FHJ ≅ ∆HFG. Find the values of
x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
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Use the Third Angles Theorem
ARCHITECTURE A drawing of a
tower’s roof is composed of
congruent triangles all converging
at a point at the top. If ∠IJK ≅ ∠IKJ
and m∠
∠IJK = 72, find m∠
∠JIH.
∆JIK ≅ ∆JIH
m∠IJK + m∠IKJ + m∠JIK = 180
m∠IJK + m∠IJK + m∠JIK = 180
72 + 72 + m∠JIK = 180
144 + m∠JIK = 180
m∠JIK = 36
m∠JIH = 36
TILES A drawing of a tile contains a series of
triangles, rectangles, squares, and a circle.
∠KML = 47.5,
If ∆KLM ≅ ∆NJL, ∠KLM ≅ ∠KML, and m∠
find m∠
∠LNJ.
A. 85
B. 45
C. 47.5
D. 95
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Prove That Two Triangles are Congruent
Write a two-column proof.
Given: ∠ ≅ ∠, ≅ , ≅ , ≅ Prove: ∆LMN ≅ ∆PON
Prove That Two Triangles are Congruent
Given: ∠ ≅ ∠, ≅ , ≅ , ≅ Prove: ∆LMN ≅ ∆PON
Proof:
Statements
1. ∠ ≅ ∠, ≅ ,
Reasons
1. Given
≅ , ≅ 2. ∠LNM ≅ ∠PNO
2. Vertical Angles Theorem
3. ∠M ≅ ∠O
3. Third Angles Theorem
4. ∆LMN ≅ ∆PON
4. Definition of Congruent
Polygons
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Find the missing information in the following proof.
Prove: ∆QNP ≅ ∆OPN
Proof:
Statements
Reasons
1. Given
2. Reflexive Property of
Congruence
3. ∠Q ≅ ∠O, ∠NPQ ≅ ∠PNO 3. Given
Angles
4. ∠QNP ≅ ∠ONP
? Theorem
4. Third
_________________
1.
2.
5. ∆QNP ≅ ∆OPN
5. Definition of Congruent Polygons
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