Book I, Proposition 6
Back to Proposition 6.
1. Complete the following with either "must be true," "must be false," 1. or "may be true or false."
To see the answer, pass your mouse over the colored area.
1. a) In a valid argument, if the hypothesis is true, then the conclusion
must be true.
1. b) In a valid argument, if the conclusion is false, then the hypothesis
must be false.
2. a) What is meant by reductio ad absurdam?
Reduction to the absurd. This is how to disprove a statment by showing that, when carried to its logical conclusion, the statement leads to an absurdity.
2. b) When do we use reductio ad absurdam, that is, what is the statement
The contradiction of what we want to prove !
3. a) State the hypothesis of Proposition 6
Two angles of a triangle are equal.
2. b) State the conclusion.
The sides opposite those angles are equal.
2. c) Practice Proposition 6.
4. Name three ways of proving straight lines equal to one another.
They are radii of a circle.
They are corresponding sides of congruent triangles.
They are the sides of an isosceles triangle.
5. Name three ways of proving angles equal to one another.
They are corresponding angles of congruent triangles.
They are the base angles of an isosceles triangle.
They are right angles. (Postulate 4.)
6. In triangle ABC, angle B is equal to angle C, the point D falls
(Prove that triangles ADB, ADC are congruent.)
Since angle B is equal to angle C, then the sides opposite them, the sides AB, AC, are equal.
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