“Education is our passport to the future, for tomorrow belongs to the people who prepare for it...
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Transcript of “Education is our passport to the future, for tomorrow belongs to the people who prepare for it...
![Page 1: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/1.jpg)
“Education is our passport to the future, for tomorrow belongs to the people who prepare for it today.”
― Malcolm X
Do NowPut 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
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Parallel Lines and Transversals
![Page 3: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/3.jpg)
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)
![Page 4: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/4.jpg)
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
![Page 5: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/5.jpg)
Draw this in your notes
∠1 = ∠3 = ∠5 = ∠7 and ∠2 = ∠4 = ∠6 = ∠8
![Page 6: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/6.jpg)
Linear PairsPairs 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.
![Page 7: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/7.jpg)
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).
![Page 8: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/8.jpg)
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.
![Page 9: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/9.jpg)
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.
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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
![Page 11: “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.](https://reader033.fdocuments.us/reader033/viewer/2022061516/56649f1f5503460f94c36e0c/html5/thumbnails/11.jpg)
Determine the values of angles A, B, C,
and D, in the figure below. Assume that the horizontal lines are
parallel.
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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<4.• Find m<3+m<4.
3. Name the relationship between <1 and <4.
4. Name the relationship between <1 and <2.