Year 2 Warm Up

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Year 2 Warm Up

• For 1-2 find the rule, then find the next three
  terms in the sequence.
• 1. 2 ,-4,-10, -16, -22
• 2. -8, -4, 0, 4, 8
• 3. Find the slope of (-8, 7) and (-8, 6)
• 4. Find the slope of (-2, 7) and (-8, 7)

1. -6 -28,-34,-40
2. 4 12,16,20
3. undefined
4. m0
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2.5 Angle Relationships

• Investigation 1 The Linear Pair Conjecture
• Step 1) Draw PQ with point R between points P and
  Q.
• Step 2) Draw RS Now you have a Linear Pair
• Step 3) Label the angles lt1 and lt2.
• Step 4) Use your protractor to measure lt1 and lt2.
• Step 5) Compare your results for your two angles
  measures with your group or a classmate.
• What do you notice about the two angles?

Linear Pair Conjecture
3
Angle Relationships

• Linear Pair Conjecture If two angles form a
  linear pair, then the measures of the angles add
  up to 180 degrees.

1
2
lt1lt2180
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Angle Relationships

• Investigation 2 Vertical Angles Conjecture
• Step 1) Draw two intersecting lines that are not
  perpendicular onto patty paper. Label the angles
  as shown
• Which angles are vertical?
• Step 2) Fold the patty paper so that one pair of
  vertical angles lie over each other.

Vertical Angles Conjecture
5

• What do you notice about their measure?
• Vertical Angles Conjecture If two angles are
  vertical angles, then they are congruent.

lt1lt3
lt2lt4
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Find the missing measures

• Ex 1)

a b c
50 130 50
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Find the missing measures

• Ex 2)

a b c
90 25 90
8
Find the missing measures

• Ex 3)

a b c d
30 100 50 100
b
c
a
30
50
d
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Algebra with Angles Ex 1

• State the type of angles
• State the relationship
• Solve for x.
• Then find measure of each angle.

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Answer 1

• The angles are vertical, therefore they are
  congruent. This means that the measures of each
  angle are equal.
• mlt1 mlt2
• 3x-40 2x 10
• x 40 -10
• x 30

Step 1 Set up the angle relationship.
Step 2 Substitute in values.
Step 3 Solve for x.
Step 4 Plug back in to find angle measures.
mlt1 3(30) - 40 mlt2 2(30) - 10
mlt1 50 mlt2 50
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Algebra with Angles Ex 2

1. State the type of angles
2. State the relationship
3. Solve for x
4. Find the measure of angle 1.

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Answer Ex. 2

• lt1 and lt2 form a line making them a linear pair
  which adds up to 180 degrees.
• Therefore, mlt1 lt2 180
• (4x 20) (x) 180
• 5x 20 180
• 5x 200
• x 40
• mlt2 40, mlt1 140

Step 1 Set up the angle relationship.
Step 2 Substitute in values.
Step 3 Solve for x.
Step 4 Plug back in to find angle measures.
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Summary Make a chart below showing the angle
types(vertical, linear pair, and right angles),
their relationships(congruent, supplementary,
complementary), and a sketch for each.
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Homework
In Class Practice
Classwork 2.5 Worksheet and Bookwork p. 122
1-6you must copy the pictures and show your
work!!!

• Homework 2.5 worksheet