1. What are the common properties of all polygons?
All polygons should first of all be closed, and have at least 3 sides. It should have no sides intersecting and crossing, and the sides have to be straight. REGULAR polygons would have at least 3 equal length sides with all equal angles.
2. What does the measure in degrees tell you about an angle? What are some common benchmark angles?
The measure in degrees of an angle tell me if the angle is either acute (below 90 degrees), right (exactly 90 degrees), obtuse (above 90 degrees), or reflex (above 180 degrees). Some common benchmark angles are 30 (1/12 of 360), 45 (1/8 of 360), 90 (1/4 of 360), and 180 degrees (1/2 of 360). These are the fundamental angles that will cover a lot of possible angles, and help us reach as close as possible to the angle we want to locate.
3. What strategies can be used to estimate angle measures? To deduce angle measures from given information? To find accurate measurement with tools?
Sometimes the benchmarks told above help us land exactly on the angle. It depends on what the angle is. If it is a multiple of 30, 45, 90 or 180, then we straight away know that we should use the benchmark which the angle is a multiple of. That would give the exact location of the angle. If the angle we are looking for isn't a multiple of any of the benchmark angles, then we would figure out which benchmark it is closest to. Usually the smaller benchmark angles like 30 degrees make finding the angle easier because the range the angle is between would be less than 90 degrees or 180 degrees, for example. To deduce the angle from the given information, we can apply our strategy of trying to find the benchmark closest to the angle we want to locate. Then, seeing how much farther the angle is from the benchmark range, we can make a logical conclusion of where the angle is located. There are also many tools that give the accurate measurement. For example, if you want to check your logical conclusion, you can use a protractor. Protractors will give the accurate measurement, and also help you understand how far apart your other strategies were from the real measurement. Angle rulers also help draw out the accurate angle.
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| This is a comparison showing what a polygon should and shouldn't look like |
2. What does the measure in degrees tell you about an angle? What are some common benchmark angles?
The measure in degrees of an angle tell me if the angle is either acute (below 90 degrees), right (exactly 90 degrees), obtuse (above 90 degrees), or reflex (above 180 degrees). Some common benchmark angles are 30 (1/12 of 360), 45 (1/8 of 360), 90 (1/4 of 360), and 180 degrees (1/2 of 360). These are the fundamental angles that will cover a lot of possible angles, and help us reach as close as possible to the angle we want to locate.
3. What strategies can be used to estimate angle measures? To deduce angle measures from given information? To find accurate measurement with tools?Sometimes the benchmarks told above help us land exactly on the angle. It depends on what the angle is. If it is a multiple of 30, 45, 90 or 180, then we straight away know that we should use the benchmark which the angle is a multiple of. That would give the exact location of the angle. If the angle we are looking for isn't a multiple of any of the benchmark angles, then we would figure out which benchmark it is closest to. Usually the smaller benchmark angles like 30 degrees make finding the angle easier because the range the angle is between would be less than 90 degrees or 180 degrees, for example. To deduce the angle from the given information, we can apply our strategy of trying to find the benchmark closest to the angle we want to locate. Then, seeing how much farther the angle is from the benchmark range, we can make a logical conclusion of where the angle is located. There are also many tools that give the accurate measurement. For example, if you want to check your logical conclusion, you can use a protractor. Protractors will give the accurate measurement, and also help you understand how far apart your other strategies were from the real measurement. Angle rulers also help draw out the accurate angle.
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