Skip to Main Content
The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
EXAMPLE 3.4
The following definitions are equivalent:
i. A triangle is an isosceles triangle if it has two equal sides.
ii. A triangle is an isosceles triangle if it has two equal angles.
Proof: Part 1. If i, then ii.
We have to prove that if a triangle has two equal sides, then it has two equal angles.
AD
C
B
Suppose that the two sides AC and CB are equal. Consider the two triangles ADC and CDB, obtained by
constructing the segment CD, perpendicular to the base AB (this is the third side not mentioned in the
hypothesis). The angles ADC and BDC are equal, because they are right angles.
The two triangles have two equal sides: CD, because it is a common ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Discrete Structures, Logic, and Computability, 4th Edition

Discrete Structures, Logic, and Computability, 4th Edition

James L. Hein

Publisher Resources

ISBN: 9780123822178