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1-4 Measuring Angles

1-4 Measuring Angles. Objective: To find and compare measures of angles. Angles. Definition : formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. How to Name it : its vertex, a point on each ray and the vertex, a number

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1-4 Measuring Angles

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  1. 1-4 Measuring Angles Objective: To find and compare measures of angles.

  2. Angles • Definition: formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. • How to Name it: its vertex, a point on each ray and the vertex, a number • Example: ∠B ∠ABC ∠CAB ∠1 A C 1 B

  3. Naming Angles What are the two other names for ∠1 and ∠2 ? L N 1 2 M P

  4. Postulate 1-7Ruler Postulate A O B Consider OB and a point on one side of OB. Every ray of the form OA can be paired one to one with a real number from 0 to 180.

  5. Protractor Postulate D C d c O The measure of ∠COD is the absolute value of the difference of the real numbers paired with OC and OD. That is, if OC corresponds with c, and OD corresponds with d, then m∠COD= | c – d| .

  6. Types of Angles Right Acute 0˚ < x < 90˚ x = 90˚ x = 180˚ Obtuse 90˚ < x < 180˚ Straight

  7. Measuring and Classifying Angles J M L H N What are the measures of ∠LKN, ∠NKM, and ∠JKN? Classify each angle as acute, right, obtuse, or straight.

  8. Congruent Angles When angles have the same measure, they are said to be congruent angles. 2 55˚ 55˚ 1 ∠1 ≅ ∠2 “angle 1 is congruent to angle 2” m∠1 = m∠2 “the measure of angle 1 is equal to the measure of angle 2

  9. Postulate 1-7Angle Addition Postulate If point Bis in the interior of ∠AOC, then m∠AOB+ m∠BOC= m∠AOC. A B O C

  10. Using the Angle Addition Postulate Find m∠SOPand m∠POT, when m∠SOT= 100˚. S P 2n + 4 3n - 19 O T

  11. Using the Angle Addition Postulate If m∠WXY= 160˚, what are m∠WXZand m∠ZXY? Z Y 7x - 4 5x + 8 W X

  12. Using the Angle Addition Postulate ∠DEF is a straight angle. What are m∠DECand m∠CEF? C 2x + 10 11x - 12 D F E

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