Book I. Proposition 20

Problems

1. a) State the hypothesis of Proposition 20.

1. b) State the conclusion.

1. c) Practice Proposition 20.

2.	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?

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.

4.	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?

5. A scalene triangle has one side that is 2 cm. Can the remaining sides
5. be multiples of 2 cm?

Questions or comments?