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Perry High School
Geometry: Week 12
Monday: Exam 3b
Tuesday: 4.1
Wednesday: 4.1
Thursday: 4.2
Friday: 4.2
Next Week: 4.3, 4.4, 4.5
Kevin M. Bond, PHD
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Perry High School
Monday: Mindfulness Training
This week: Body Scan
http://marc.ucla.edu/mpeg/Body-ScanMeditation.mp3
Kevin M. Bond, PHD
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Perry High School
Exam 3b
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Perry High School
Tuesday: Mindfulness Training
This week: Body Scan
http://marc.ucla.edu/mpeg/Body-ScanMeditation.mp3
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Perry High School
Start Chapter 4
Congruent Triangles
• Show which or when
two or more triangles
are identical.
• Applied uses of
congruent triangles
• Turn in 4.1 Today
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Perry High School
Monday: 4.1, Triangles and Angles
Goals
1. Classifying Triangles
2. Using Angle
Measures of
Triangles
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Classifying Triangles
Triangle – a polygon formed by three segments
joining three noncollinear points.
• Also Known as TRIGON
Note: Triangles are classified by sides and angles
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Classifying Triangles, by Sides
See page 194
• Equilateral Triangles
–
•
Isosceles Triangles
–
•
Three congruent sides
At least 2 congruent sides
Scalene Triangles
–
No congruent sides
Note: Markings on diagrams that show congruence
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Classifying Triangles, by Angles
See page 194
• Acute
–
•
Equiangular
–
•
3 congruent angles
Right
–
•
Three acute angles
1 right angle
Obtuse
–
1 obtuse angle
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Example 1, page 194
Classifying angles
Be specific, e.g., angle
id then side id.
a. ⊿ABC
b. ⊿DEF
Video: Euclid
https://www.youtube.
com/watch?v=rdNfO
mEiNzs
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Definitions
Vertex – of a triangle,
each of the three
points joining the
sides
Adjacent Sides – of a
triangle, two sides
sharing a common
vertex
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Definitions
In an Isosceles Triangle
Legs – the two
congruent sides of
an isosceles triangle
Base – the third side of
the isosceles triangle
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Example 2, page 195
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Angle Measures of Triangles
Interior Angles – the
three original angles
of a triangle
“inside” the triangle
Exterior Angles – the
angles formed by
extending the lines
in a triangle;
adjacent to the
interior angles
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Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle
is 180 degrees.
Proof: Page 196
• Parallel Postulate –
• Angle Addition Postulate –
• Definition of Straight Angle –
• Alternate Interior Angles Theorem –
• Definition of Congruent Angles –
• Substitution Property of Equality -Kevin M. Bond, PHD
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Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to
the sum of the measures of the two nonadjacent interior
angles.
Proof: Left as exercise
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Example
In a right triangle, the
two non-right angles
are 2x and x. What
are their degree
measure?
Process:
1. Draw a diagram
2. Make an equation
3. Solve
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Perry High School
4.1 Practice Day
Day 1 (Today)
4.1 p. 198
1-9
Mixed Review 52-68
Day 2
Universe of Triangles
Check: 1-9, 42, 50
Finish:
10-15
16-43 Even, not 40
45-47
52-66 Even
Show D2 when completed
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Perry High School
Wednesday:
Mindfulness Training
This week: Body Scan
http://marc.ucla.edu/mpeg/Body-ScanMeditation.mp3
Kevin M. Bond, PHD
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Perry High School
4.1 Work Day
Day 1
Day 2 (Today)
Universe of Triangles
4.1 p. 198
1-9
Mixed Review 52-68
4.1 p. 198
10-15
16-43 Even, not 40
45-47
Show D2 when completed
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Perry High School
Thursday:
Mindfulness Training
This week: Body Scan
http://marc.ucla.edu/mpeg/Body-ScanMeditation.mp3
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Questions on 4.1?
Meditate
Questions?
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4.2: Congruence and Triangles
Two geometric figures are congruent if they have exactly
the same size and shape.
• Corresponding angles are congruent and
• Corresponding sides are congruent
WRT Triangles: Corresponding parts of congruent
triangles are congruent. (CPCTC)
OR: Corresponding parts of congruent triangles are equal.
(CPCTE)
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Congruent v. Similar
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Name Congruent Parts
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Examples
Page 202: 1. Naming Congruent Parts
Page 203: 2. Using Properties of
Congruent figures
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Third Angle Theorem
If two angles of one triangle are congruent to
two angles of another triangle, then the
third angles are also congruent.
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CPCTC
• Corresponding parts of congruent triangles
are congruent.
• To show triangles are congruent, show
that corresponding parts are congruent.
Note: Sometimes see this as CPCTE;
Note: Congruent ≡ Equal Measure
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Practice
• Decide whether the triangles are
congruent. Justify.
86
86
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Properties of Congruent Triangles
Page 205
• Reflexive Property of Congruent Triangles
• Symmetric Property of Congruent
Triangles
• Transitive Property of Congruent Triangles
• CPCTE
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4.2 Practice
Day 1 (Today)
4.2 p. 205
Day 2
Review: 1-9; 53; 57
1-9
41-57
10-28 even
39
42-56 even
Quiz 1: 1-6
Show D2 When
Completed
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Perry High School
Friday: Mindfulness Training
This week: Body Scan
http://marc.ucla.edu/mpeg/Body-ScanMeditation.mp3
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Perry High School
4.2 Work Day
Day 1
4.2 p. 205
Day 2 (Today)
4.2 p. 205
1-9
41-57
10-28 even
30-34
36-37, 39
Quiz 1: 1-6, p. 210
Show D2 When Completed
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