Geometry Notes

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Geometry Notes

• Sections 2-8

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What youll learn

• How to write proofs involving supplementary and
  complementary angles
• How to write proofs involving congruent and right
  angles

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Vocabulary

• There is no new vocabulary
• However. . . Do you know these definitions. . .?
• Supplementary Angles
• Complementary Angles
• Reflexive Property
• Symmetric Property
• Transitive Property
• Perpendicular lines
• Linear Pair of Angles
• Vertical Angles
• Congruent Angles

• Adjacent Angles
• Congruent Segments
• Angle Addition Postulate
• Segment Addition Postulate
• Midpoint
• Segment Bisector
• Angle Bisector
• Opposite Rays
• I hope so. . . .

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Congruence of Segments is . . .



A segment is congruent to itself. AB ? AB
Reflexive ? segments
You can switch the left and right sides If AB ?
CD then CD ? AB.
Symmetric ? segments
If AB ? CD and CD ? EF, then AB ? EF.
Transitive ? segments
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Congruence of Angles is . . .



An angle is congruent to itself. ?A ? ?A
Reflexive ? angles
You can switch the left and right sides If ?A ?
?B then ?B ? ?A.
Symmetric ? angles
If ?A ? ?B and ?B ? ?C, then ?A ? ?C.
Transitive ? angles
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Supplement Theorem

• If two angles form a linear pair,
• then they are supplementary.

• two angles form a linear pair,

• they are supplementary

• What are we given?
• Look in the hypothesis of the conditional
  statement and draw it.
• Now what can we conclude?
• Look in the conclusion of the conditional
  statement
• ?1 and ?2 are supplementary.

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How does this work in problems?
If ?1 and ?2 form a linear pair and m?2 67,
find m?1.

• Linear pairs ? supplementary ? add up to 180?

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More example problems
Find the measure of each angle.

• Linear pairs ? supplementary ? add up to 180?

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More example problems
Find the measure of each angle.

• Linear pairs ? supplementary ? add up to 180?

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Vertical Angles

• Weve done this before.
• Draw two vertical angles
• If two angles are vertical angles then they are
  congruent.

• Vert. ?s ? ? ?

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How does this work in problems?
If m?2 72, find m?1.
1
2

• Vert. ?s ? ? ?

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More example problems
Find the measure of each angle.

• Vert. ?s ? ? ?

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More theorems. . .

• Complement theorem
• If the noncommon sides of two adjacent angles
  form a right angle, then the angles are
  complementary angles.

?1 ?2 complementary ? m ?1 m ?2 90
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More theorems. . .

• Angles supplementary to the same angle or to two
  congruent angles are congruent.

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More theorems. . .

• Angles complementary to the same angle or to two
  congruent angles are congruent.

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More theorems. . .

• Perpendicular lines intersect to form four right
  angles.
• All right angles are congruent.
• Perpendicular lines form congruent adjacent
  angles.
• If two angles are congruent and supplementary,
  then each angle is a right angle.
• If two congruent angles form a linear pair, then
  they are right angles.

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Have you learned .. . .

• How to write proofs involving supplementary and
  complementary angles?
• How to write proofs involving congruent and right
  angles?
• Assignment Worksheet 2.8A