Monday, December 14, 2015
Our goals for the lesson.
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| We went over types of triangles. We know that triangles ALWAYS equal 180°. Equilateral: 180° divided by 3 angles gives us 60° each. Isosceles: Two angles are the same, therefore the bottom right angle is 70° as well. We can add those and subtract by 180° to get 40°. Obtuse: We are given 120° and 25°, if we add those and subtract by 180° we get 35° |
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| We went over parallel lines and a transversal (a transversal runs through two parallel lines. The bottom diagram shows two parallel lines with a transversal and also a triangle. We identified each angle with strategies (this is in your work book pg. 153) |
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| We went over the three patterns that help us with solving problems involving angles. C pattern can help us solve interior angles (interior angles equal 180°). F pattern can help us solve corresponding angles. Z pattern can help us solve alternate angles. Remember sometimes these letters can look backwards or upside down! So turn your paper and get a different perspective sometimes. |
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| Whole class problem solving question. Even though it looks like we were only given 45°, we were actually told about a 90° angle too in the corner! With that we can solve B because it sits on a straight line, so we know B will be 90° too. We did our Z pattern to find the alternate angles to find angle E. We found out A was 45° too because A and E are complementary (they equal 90° together). We found C because we had angles D and B so we can find out C is 45° (inside of a triangle). We can find F because it is supplementary to C (meaning C and F will equal 180°). |
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| We were given angle k 110° and also a 90° angle. We can use supplementary angles to find out h is 70°. Because k and h sit on a 180° line, if you subtract 110° from 180° you will get 70°. We can use our knowledge of opposite angles to find out f and g. We can use our F pattern to find our a and b We can use opposite angles to find c (opposite of a). We can find out e because it is the inside of a triangle. We add 90° and 70° and subtract 180° to get 20°. We can use the Z pattern to find out that d is also 20°. |
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| We are given 58°, 53°, and a right angle. We can use our right angle to find that v is 90°. Now we have two angles of a triangle and can add 58° + 90° - 180° to find that angle t is 32°. We can use our Z pattern to find that u = 58°. Now we have two angles of another triangle. And can add 58° + 53° - 180° to find w = 69°. We can see and w and y are supplementary angles (they sit on a 180° line). So we can subtract 69° from 180° to find that y = 111° Now we have two angles (x and y) of the last and bottom triangle if we add 32° + 111° - 180° we can find that z = 37°. |
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How to construct a perpendicular bisector
How to construct an angle bisector
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