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1.4 Angles and Measures

1.4 Angles and Measures. Angle Addition Postulate Classify angles. Definition of an angle. Two rays that have the same initial point ca lled the Vertex Named ∠ABC A All angles are named with three letters. B The middle letter is the vertex. C.

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1.4 Angles and Measures

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  1. 1.4 Angles and Measures Angle Addition Postulate Classify angles

  2. Definition of an angle Two rays that have the same initial point called the Vertex Named ∠ABC A All angles are named with three letters. B The middle letter is the vertex. C

  3. Angle Measure We use a protractor to measure angles and is given a letter m before the name when standing for its measure. m∠ABC = 50ᵒ, so the angle has ameasurement of 50 degrees.

  4. The Protractor Postulatelike the Ruler postulate for angles • The measure of an angle is the absolute value of the different of the terminal side and the initial side. X terminal side 50 ᵒ Y Initial side Z

  5. Angles can be also be Congruent Again the definition of Congruent is Same Shape and Same Size. If m∠XYZ = m∠ABC, then ∠XYZ≌∠ABC. If ∠PQR≌∠FMB, then ∠PQR≌∠BMF, but not ∠PQR≄∠MBF. Order is important! The vertex must be in the middle

  6. Angles have an Interior and an Exterior K Q Interior Exterior X

  7. The Angle Addition Postulate If P is in the interior of ∠RST, then m∠RSP + m∠PST = m∠RST T m∠TSP = 12ᵒ P m∠PSR = 24ᵒ S R m∠RST = 36ᵒ

  8. Classifying Angles Acute Right Obtuse 0 to less then 90ᵒ degrees More then 90ᵒ degrees 90ᵒ degrees Straight Angle equals 180ᵒ

  9. Adjacent Angles Adjacent means next to each other; the same as adjacent lockers. Adjacent lockers share one wall. Adjacent angles share one side and have a common vertex. ∠ABC and ∠CBX are A C adjacent angles B X

  10. Homework Page 29 – 31 #17 – 22, 26- 34, 38, 41, 42, 51-53

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