Determining the Conditions under which Lines and Segments are Parallel or Perpendicular

Math

1. Determining The Conditions Under Which Lines and Segments are Parallel or Perpendicular

2. Learning Targets: a. Identify the lines and segments as to parallel, perpendicular, or intersecting. b. Solve for the missing angles .

3. PARALLEL

4. If two lines are cut by a transversal, then the two lines are PARALLEL if : a . Corresponding angles are congruent . b. Alternate interior angles are congruent . c. Alternate exterior angles are congruent . d. Interior angles on the same side of the transversal are supplementary . e. Exterior angles on the same side of the tramsversal are supplementary .

5. m<d = (2x + 12) ° m<f = (x + 33)° Find x and all the other angles. Example:

6. m<d = (2x + 12) ° m<f = (x + 33)° <d + <f = 180 (2x+12) + (x+33) = 180 2x+x+12+33 = 180 3x+45 = 180 3x = 180 – 45 3x = 135 3x = 135 3 3 x = 45 ° Solution: angle d and angle f are same-side interior angles

7. <d = 2x+12 <f = x+33 <d = 2(45)+12 <f = 45+33 <d = 90+12 <f = 78 ° <d = 102° Since: x = 45 °, then

8. PERPENDICULAR

9. Two lines are PERPENDICULAR if one of these theorems is true: They form four right angles . If the angles in a linear pair are congruent . If two angles are adjacent and complementary .

10. INTERSECTING

11. ACTIVITY A. Tell whether the lines are perpendicular, parallel, or intersecting . 1. 2. 3.

12. 4. 5. 6.

13. B . Find the value of x and all the other angles. Given: <1 = (3x – 70) ° <8 = (2x + 5)°