Question 201372This question is from textbook Discovering Geometry An Investigative Approach
: 1) why does constructing an equilateral triangle is easy by just copying the given equilateral triangle?
2)In a triangle, what is longer: a median or an altitude? Are they ever the same length? Explain your answers.
3) how can you measure angle by not using your protectors?
pls help me... its due monday pls.
This question is from textbook Discovering Geometry An Investigative Approach
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 1) to construct a new equilateral triangle of side "s", start with the existing equilateral triangle, Extend 2 sides until they are "s" long, connect these points.
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2)altitude is perpendicular distance from the vertex to the opposite side
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Median is the distance from the vertex to the opposite side
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They are equal in isosceles(when base is odd length) or equilateral triangles
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3)Construction easily makes 180 degree and 90 degree angles.
bisection or repeated bisection yields, 45, 22.5, 11.25, etc angles
Adding or subtracting from each other yields combinations.
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a 30-60-90 triangle has sides of 1-2-sqrt3. Constructing a 30 degree or 60 degree is readily done using length ratios of 1 &2. Bisecting these repeatedly yields 15, 7.5, 3.75, etc. degrees. These can be added or subtracted to find numerous angles.
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