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Angles

Angles. Angle. An object that has two rays (called sides ) with a common endpoint (called the vertex ). A. B. C. Example 1. Name each of the following: Sides:_____________________ Vertex:_________ Name:_____________________. Interior of an Angle.

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Angles

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  1. Angles

  2. Angle An object that has two rays (called sides) with a common endpoint (called the vertex).

  3. A B C Example 1 Name each of the following: Sides:_____________________ Vertex:_________ Name:_____________________

  4. Interior of an Angle the space between the rays that create an angle.

  5. Exterior of an Angle the space that is outside of the rays

  6. R Q S P Example 2 How does the diagram in EXAMPLE 1 differ from the diagram in this example?

  7. R Q S P Example 3 A) Name a point in the interior of QPS in EXAMPLE 2. B) Name a point in the exterior of QPR in EXAMPLE 2.

  8. Adjacent To be next to. SHARING a side.

  9. Angle Addition Postulate The sum of two adjacent angles is equal to the largest angle.

  10. R Q S P If R is in the interior of QPS, then mQPR + mRPS = mQPS. ANGLE ADDITION POSTULATE: If mQPR + mRPS = mQPS, then R is in the interior of QPS.

  11. R Q S P If R is in the interior of QPS, then mQPR + mRPS = mQPS. ANGLE ADDITION POSTULATE: If mQPR + mRPS = mQPS, then R is in the interior of QPS.

  12. P R Q S Example 4 If mPQS = 77 and mPQR = 32, then find mRQS.

  13. A B O C Example 5 If mAOC = 70, mAOB =(x + 10), and mBOC =x, find: x = __________ mBOC = _______________ mAOB = _______________

  14. Acute Angle An angle measuring less than 90°

  15. Right Angle An angle whose measure is exactly 90°

  16. Obtuse Angle An angle measuring greater than 90° but less than 180°

  17. Straight Angle An angle measuring exactly 180°

  18. Y L 125 F 35 I T C NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ R T X S N S NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ For each of the following angles A) Name it. B) Tell whether its measure is <90, >90, =90, or = 180. C) Classify it.

  19. Congruent to be the same shape and same size.

  20. Angle Bisector a line, ray, or segment that divides an angle into two congruent angles.

  21. W X Z Y Example 7 If XZ is an angle bisector of WXY, name the two congruent angles that it forms.

  22. E G I F H Example 8 FG bisects EFH. Find the value of x. m EFG = (5x – 10); m GFH = (3x + 25)

  23. E G I F H Example 9 FG bisects EFH. Find the value of x. m GFH = (3x + 20); m EFH = (4x + 80)

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