Book I. Proposition 20
1. a) State the hypothesis of Proposition 20.
These are any two sides of a triangle.
1. b) State the conclusion.
Together they will be greater than the third side.
1. c) Practice Proposition 20.
||In an equilateral triangle, the sides are in the ratio 1 : 1 : 1; that is, they are equal to one another. How does that illustrate Proposition 20?
||1 + 1 is greater than 1.
3. a) Can an isosceles triangle have sides in the ratio 1 : 1 : 2?
No. The equal sides 1 + 1 are not greater than 2.
| 3. b)
||Can an isosceles triangle ever have sides in the ratio of natural numbers?
||Yes, if the unequal side is less than the equal sides. For example, 2 : 2 : 1.
||Let the perimeter of a scalene triangle be a natural number of units. What is the smallest perimeter such that the sides will be in the ratio of natural numbers?
2 : 3 : 4
5. A scalene triangle has one side that is 2 cm. Can the remaining sides
5. be multiples of 2 cm?
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