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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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