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Proposition I.6 If two angles in a triangle are equal the sides opposite these angles are also equal.

Proposition I.6 If two angles in a triangle are equal the sides opposite these angles are also equal.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.1: Congruent Triangles
Problem 8E: a. Suppose that you wish to prove that RSTSRV. Using the reason Identity, name one pair of...
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3. Proposition I.6 is the converse of Thales' theorem about the base angles of an isoceles triangle being equal which is Proposition I.5 of the Elements. Proposition I.6 is the first time in Elements that Euclid uses proof by contradiction, reductio ad absurdum. Complete the following proof by showing that ADBC is congruent to AACB which contradicts the fact that ADBC is inscribed within AACB. As Euclid would put it the less cannot be equal to the greater. Technically this is a double reductio ad absurdum argument and you must also show that the second case where AB < AC also leads to a contradiction. You may finish this argument with the tried and true "it can be shown by a similar argument that the assumption AB < AC also leads to a contradiction therefore.. Proposition I.6 If two angles in a triangle are equal the sides opposite these angles are also equal. A Proof Assume AABC has ZB = 2C but AB + AC. Then either AB > AC or AB < AC. Assume AB > AC. Then we construct a point D on AB so that DB = AC. B
Transcribed Image Text:3. Proposition I.6 is the converse of Thales' theorem about the base angles of an isoceles triangle being equal which is Proposition I.5 of the Elements. Proposition I.6 is the first time in Elements that Euclid uses proof by contradiction, reductio ad absurdum. Complete the following proof by showing that ADBC is congruent to AACB which contradicts the fact that ADBC is inscribed within AACB. As Euclid would put it the less cannot be equal to the greater. Technically this is a double reductio ad absurdum argument and you must also show that the second case where AB < AC also leads to a contradiction. You may finish this argument with the tried and true "it can be shown by a similar argument that the assumption AB < AC also leads to a contradiction therefore.. Proposition I.6 If two angles in a triangle are equal the sides opposite these angles are also equal. A Proof Assume AABC has ZB = 2C but AB + AC. Then either AB > AC or AB < AC. Assume AB > AC. Then we construct a point D on AB so that DB = AC. B
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