1. Do NOW
If mABD = (6x + 4)° and mDBC = (8x – 4), and 𝑺𝑷 bisects, justify using a proof.
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2. Page 24 18) 25° 19) Acute 20) Right 21) 22) Obtuse 32) 72° 41) D 42) H
29) Statements
Reasons
1) mAOC = 7x – 2, mDOC = 2x + 8 and mEOD = 27
1) Given
2) mAOC + mCOD + mDOE = mAOE
2) Given
3) (7x – 2) + (2x + 8) + 27 = 180°
3) Substitution
4) 9x + 33 = 180
– – 33
4) Combine Like Terms
5) 𝟗𝒙 𝟗 = 𝟏𝟒𝟕 𝟑𝟑
6) Substitution P.O.E.
7) x = 49/11 or 16 1/3
7) Division P.O.E.
18)
25°
19)
Acute
20)
Right
21)
22)
Obtuse
32)
72°
41) D
42) H
43) C
44) J
17) Statements
Reasons
1) mRSP = 3x – 2, mPST = 9x – 26, and 𝑺𝑷 bisects
Given
2) mRSP = mPST
2) Def’n Angle Bisector
3) (3x – 2)° = (9x – 26)°
–9x –9x
3) Substitution
4) –6x – 2 = –26
4) Subtraction P.O.E.
5) −𝟔𝒙 −𝟔 = −𝟐𝟒 −𝟔
5) Addition P.O.E.
6) x = 4
6) Division P.O.E.
7) mRST = mRSP + mPST
7) Angle Addition Post.
8) mRST = 3x – 2 + 9x – 26
8) Substitution
9) mRST = 12x – 28
= 12(4) – 28
9) Combine Like Terms
10) mRST = 20°
10) Substitution
31) Statements
Reasons
1) mAOB = 6x + 5, mBOC = 4x – 2 and mAOC = 8x + 21
1) Given
2) mAOB + mBOC = mAOC
2) Angle Addition Post.
3) 6x x – 2 = 8x + 21
3) Substitution
4) 10x + 3 = 8x + 21
– – 3
4) Combine Like Terms
5) 10x = 8x + 18
– 8x –8x
5) Subtraction P.O.E.
6) 𝟐𝒙 𝟐 = 𝟏𝟖 𝟐
6) Substitution P.O.E.
7) x = 9
7) Division P.O.E.
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3. 2/18/ :34 PM
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4. Section 1–4 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us
Pairs of Angles
Section 1–4
Geometry PreAP, Revised ©2013
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5. Definitions Vertical Angles
Adjacent angles are two angles in the same plane; Think: NEXT TO
Share the common side
Have the Same Vertex
Have no interior points
Are Coplanar
Linear Pair of angles is a pair of adjacent angle whose non–common sides are opposite rays; they are supplementary; Think: L
Vertical angles are two angles sides form two pairs of opposite rays; Think: VA
Angles
Vertical
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6. Visual Examples
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7. Example 1
Identify all of the vertical angles, adjacent angles, and linear pairs of angles in the figure.
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8. Your Turn
Identify all of the vertical angles, adjacent angles, and linear pairs of angles in the figure.
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9. Example 2
Solve for x and y
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10. Example 3
Solve for c
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11. Example 4 Solve for x and m∠MAT 2/18/2019 11:34 PM
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12. Your Turn Solve for t and m∠HRN 2/18/2019 11:34 PM
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13. Example 5
Solve for x
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14. Example 6
Solve for x
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15. Your Turn
Solve for x
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16. Definitions
Complementary angles are two angles whose measures have a sum of 90°; Think: Complementary angles make a CORNER
Supplementary angles are two angles whose measures have a sum of 180°; Think: Supplementary angles make a STRAIGHT LINE
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17. Example 7 What is the complement and supplement angle of 81.2°?
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18. Example 8 What is the complement and supplement angle of (7x – 12)°?
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19. Your Turn What is the complement and supplement angle of (6x + 5)°?
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20. Example 9
An angle is 50° smaller than its supplement. Find the two angles.
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21. Example 10 An angle exceeds its complement by 10°. What is the angle?
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22. Your Turn An angle is triple its supplement. What is the angle?
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23. Example 11
An angle is 48° less than one-third its supplement. Find the two angles.
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24. Your Turn
An angle is 26° less than one-fourth its supplement. Find the two angles.
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25. Example 5 Solve for x and m∠GEO and justify with a proof
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26. Example 5 Solve for x and m∠GEO and justify with a proof
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