“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 Write down the vertical angles conjecture
Parallel Lines and Transversals
Parallel Lines Two lines are said to be parallel if 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)
Transversal A third line that crosses a pair of parallel lines on a slant 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 As the transversal crosses the two parallel lines, eight angles are formed
Draw this in your notes ∠ 1 = ∠ 3 = ∠ 5 = ∠ 7 and ∠ 2 = ∠ 4 = ∠ 6 = ∠ 8
Linear Pairs Pairs of adjacent angles are supplementary (always add up to 180 o), as you can see from the figure. Thus ∠ 1 + ∠ 2 = 180 o, ∠ 2 + ∠ 3 = 180 o, ∠ 3 + ∠ 4 = 180 o, ∠ 5 + ∠ 6 = 180 o, etc.
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).
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.
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 exterior angles. Alternate exterior angles are congruent.
Vertical Angles When two lines cross they form four 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
Determine the values of angles A, B, C, and D, in the figure below. Assume that the horizontal lines are parallel. Determine the values of angles A, B, C, and D, in the figure below. Assume that the horizontal lines are parallel.
Exit Slip 1.Give a counterexample to this statement: “If two angles are supplementary, then they are congruent.” 2.Use the diagram at the right Find m<1+m<2. Find m<1+m<2. Find m<4. Find m<4. Find m<3+m<4. Find m<3+m<4. 3. Name the relationship between <1 and <4. 4. Name the relationship between <1 and <2.