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Prove and use theorems about the angles formed by parallel lines and a transversal.

Objective. Prove and use theorems about the angles formed by parallel lines and a transversal. Alternate Interior <s Th. - (inside & opposite sides of transversal) <2  <7 <3  <6 Alternate Exterior <s Th. -(outside & opposite sides of transversal) <1  <8

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Prove and use theorems about the angles formed by parallel lines and a transversal.

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  1. Objective Prove and use theorems about the angles formed by parallel lines and a transversal.

  2. Alternate Interior <s Th. - (inside & opposite sides of transversal) <2  <7 <3  <6 Alternate Exterior <s Th. -(outside & opposite sides of transversal) <1  <8 <4  <5 Same side interior <s Th. -(inside & same side of transversal) <2 + <3 =180° <6 + <7 = 180°

  3. Check It Out! Example 1 Find mQRS. x = 118 Corr. s Post. mQRS + x = 180° Def. of Linear Pair Subtract x from both sides. mQRS = 180° – x = 180° – 118° Substitute 118° for x. = 62°

  4. Helpful Hint If a transversal is perpendicular to two parallel lines, all eight angles are congruent.

  5. Example 2: Finding Angle Measures Find each angle measure. A. mEDG mEDG = 75° Alt. Ext. s Thm. B. mBDG x – 30° = 75° Alt. Ext. s Thm. x = 105 Add 30 to both sides. mBDG = 105°

  6. Check It Out! Example 2 Find mABD. 2x + 10° = 3x – 15° Alt. Int. s Thm. Subtract 2x and add 15 to both sides. x = 25 mABD = 2(25) + 10 = 60° Substitute 25 for x.

  7. Lesson Quiz State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m1 = 120°, m2 = (60x)° 2. m2 = (75x – 30)°, m3 = (30x + 60)° Alt. Ext. s Thm.; m2 = 120° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Alt. Int. s Thm.; m3 = 120°, m4 =120° Same-Side Int. s Thm.; m3 = 120°, m5 =60°

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