## Book I, Proposition 6Problems Back to Proposition 6. 1. Complete the following with either "must be true," "must be false," or 1. "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
Reduction to the absurd. This is how to 2. b) When do we use 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. Table of Contents | Introduction | Home Please make a donation to keep TheMathPage online. Copyright © 2012 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |