Angles Continued...

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Angles Continued...

• Honors Geometry

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4-2Note APE stands for Addition Property of
Equality

• 3)b) ?WPX and ?XPY ?WPZ and ?ZPY?WPX and
  ?ZPY?WPZ and ?XPY
• 4) linear pair, suppl., 180
• 5)b) b70, c110, d70
• 6) 30, 30, 160, 35, 90, 75, 110, 180, 75, 20
• 11)b) EACd) EAD

• 12)a) EDC, b) EDC, c) BCD, BCA, d) EAB
• 14) 100, 132, 36, 154.5, 180-n, 180-n-k, n, 90n
• 16) 135
• 18) Def. of L.P., Suppl. Post., Def. Suppl.,
  repeat a-c

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4-4

• 3)b) AAP
• 4)
• 5)b) obtused) equal
• 6) No
• 8) 70, 22, 43.5, 90-n, n, 45-n

• 10)a) ?EAC and ?CAD ?EAB and ?BAD?BAD and
  ?DACb) ?BAE and ?DAC?EAC and ?DAB?BAC and
  ?DAEc) ?EAC and ?BAD?EAB and ?CAD?BAC and ?DAE
• 12) 38

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Theorem

• Congruence is an equivalence relation
• Reflexive, Symmetric, and Transitive properties
  are true for congruence
• Refl. ?A??A
• Symm. If ?A??B, then ?B??A
• Trans. If ?A??B and ?B??C, then ?A??C

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Theorem

• If angles in a linear pair are congruent, then
  each is a right angle.

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Theorem

• If two angles are complementary, both are acute.

7
Theorem

• Any 2 right angles are congruent.

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Lets Prove the Last ThmIf ?A and ?B are right,
then ?A??B.
Q.E.D. Which stands for Quod Erat
Demonstradum or That which was to be
demonstrated
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Theorem

• If two angles are congruent and supplementary,
  then they are right angles.

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Supplement Theorem

• This is an important theorem
• Supplements of congruent angles are congruent.
• In other words
• If ?A??B, ?A ?C AND ?B ?D are supplementary,
  ?C??D (the supplements of ?A ?B).

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Supplement Theorem

• Now read the proof on pg. 102 and the 4
  paragraphs that follow on pgs. 102-103

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Complement Theorem

• This is an important theorem
• Complements of congruent angles are congruent.
• In other words
• If ?A??B, ?A ?C AND ?B ?D are complementary,
  ?C??D (the complements of ?A ?B).

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• Please start on your homework.