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1.6 Angle Pair Relationships

1.6 Angle Pair Relationships. Geometry Mrs. Spitz Fall 2005. Standards/Objectives:. Standard 3: Students will understand geometric concepts and applications. Objectives: Identify vertical angles and linear pairs. Identify complementary and supplementary angles. Assignment:.

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1.6 Angle Pair Relationships

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  1. 1.6 Angle Pair Relationships Geometry Mrs. Spitz Fall 2005

  2. Standards/Objectives: Standard 3: Students will understand geometric concepts and applications. Objectives: • Identify vertical angles and linear pairs. • Identify complementary and supplementary angles.

  3. Assignment: • pp. 47-49 #4-36 all; 41-51 odd

  4. Which angles are adjacent? 1 &  2,  2 &  3,  3 &  4,  4&  1 Then what do we call  1 &  3? Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays.  1 &  3,  2 &  4 2 1 3 4

  5. Linear Pair (of angles) • 2 adjacent angles whose non-common sides are opposite rays. 1 2

  6. Example • Vertical angles? 1 & 4 • Adjacent angles? 1 & 2, 2 & 3, 3 & 4, 4 & 5, 5 & 1 • Linear pair? 5 & 4, 1 & 5 • Adjacent angles not a linear pair? 1 & 2, 2 & 3, 3 & 4 2 1 3 5 4

  7. Important Facts • Vertical Angles are congruent. • The sum of the measures of the angles in a linear pair is 180o.

  8. Example: • If m 5=130o, find m 3 = 130° m 6 = 50° m 4 = 50° 4 5 3 6

  9. A Example: E 3x+5o y+20o B x+15o 4y-15o D • Find x y m ABE m ABD m DBC m EBC C x=40 y=35 m ABE=125o m ABD=55o m DBC=125o m EBC=55o

  10. Complementary Angles • 2 angles whose sum is 90o 35o 1 2 55o A 1 & 2 are complementary A & B are complementary B

  11. Supplementary Angles • 2 angles whose sum is 180o 1 & 2 are supplementary. X & Y are supplementary. 1 2 130o 50o X Y

  12. Ex: A & B are supplementary. mA is 5 times mB. Find mA & mB. mA + mB = 180o mA = 5(mB) Now substitute! 5(mB) + mB = 180o 6(mB)=180o mB=30o mA=150o

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