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Put your 2.5 worksheet on your desk ready to be stamped. Take a protractor from the front.

“Education is our passport to the future, for tomorrow belongs to the people who prepare for it today.” ― Malcolm X Do Now. Put your 2.5 worksheet on your desk ready to be stamped. Take a protractor from the front. Take out your compass. Write down the linear pairs conjecture

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Put your 2.5 worksheet on your desk ready to be stamped. Take a protractor from the front.

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  1. “Education is our passport to the future, for tomorrow belongs to the people who prepare for it today.” ― Malcolm XDo Now • Put your 2.5 worksheet on your desk ready to be stamped. • Take a protractor from the front. • Take out your compass. • Write down the linear pairs conjecture • Write down the vertical angles conjecture

  2. Parallel Lines and Transversals

  3. Parallel Lines • Two lines are said to be parallel if • (i) they both lie in the same plane, and, • (ii) they do not intersect (or cross each other)

  4. Transversal • A third line that crosses a pair of parallel lines on a slant • As the transversal crosses the two parallel lines, eight angles are formed

  5. Draw this in your notes ∠1 = ∠3 = ∠5 = ∠7 and ∠2 = ∠4 = ∠6 = ∠8

  6. Linear Pairs • Pairs of adjacent angles are supplementary (always add up to 180o), as you can see from the figure. • Thus∠ 1 + ∠ 2 = 180o , ∠ 2 + ∠ 3 = 180o , ∠ 3 + ∠ 4 = 180o , ∠ 5 + ∠ 6 = 180o , etc.

  7. Corresponding Angles • Angles in the same relative position around the two intersection points are called corresponding angles . • Thus ∠ 1 and ∠ 5 are corresponding angles, as are ∠ 4 and ∠ 8, • ∠ 2 and ∠ 6, and also ∠ 3 and ∠ 7. • Corresponding angles are congruent (same angle measure).

  8. Alternate Interior Angles • Alternate sides of the transversal • Inside the parallel lines • ∠3 and ∠5 are called alternate interior angles. ∠4 and ∠6 are also alternate interior angles. • Alternate interior angles are congruent.

  9. Alternate Exterior Angles • Alternate sides of the transversal • Outside the parallel lines • ∠2 and ∠8 are called alternate exterior angles. ∠1 and ∠7 are also alternate exteriorangles. • Alternate exterior angles are congruent.

  10. Vertical Angles • When two lines cross they form four angles. • ∠ 1 and ∠ 3 are said to be vertical angles • ∠ 2 and ∠ 4 also form vertical angles. • Vertical angles are congruent. • Thus∠ 1 = ∠ 3 and ∠ 2 = ∠ 4

  11. Determine the values of angles A, B, C,and D, in the figure below. Assume that the horizontal lines are parallel.

  12. Exit Slip • Give a counterexample to this statement: “If two angles are supplementary, then they are congruent.” • Use the diagram at the right • Find m<1+m<2. • Find m<4. • Find m<3+m<4. 3. Name the relationship between <1 and <4. 4. Name the relationship between <1 and <2.

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