6.5 Inequalities in Triangles and Indirect Proofs

6.5 Inequalities in Triangles and Indirect Proofs 6.5 Pear Deck Review of Inequalities in Triangles

The largest angle in a triangle is opposite the longest side. The shortest side of a triangle is opposite the smallest angle. The two shorter sides of triangle must add up to

be longer than the third side. Hinge Theorem If two sides of one triangle are congruent to two sides

of another triangle and the included angle of the first is smaller then the included angle of the second, then the third side of the first is

shorter than the third side of the second. Indirect Proof 1) Make a temporary assumption that that

desired conclusion is false. 2) Show that this assumption leads to a logical impossibility. 3) Therefore the original statement is true by contradiction.

Example of an Indirect Proof I want to prove that today is not Taco Tuesday. I first assume that today is Taco Tuesday. When I come home on Taco Tuesday, there is

usually ground beef defrosting on the kitchen table. Since there was not ground beef defrosting on the kitchen table, my original assumption must be false. Therefore, today is not Taco Tuesday : (

Use an indirect proof to show that a triangle can only have at most one right angle. Use indirect proof to show that in triangle ABC, if AB= 7 and BC = 8, then CA cannot equal 15.

Use indirect proof to show that if x and y are odd integers, then xy must be odd.

Recently Viewed Presentations

• CSE3213 Computer Network I Medium Access Control Protocols (Ch. 6.1 - 6.3) Course page: http://www.cse.yorku.ca/course/3213 Slides modified from Alberto Leon-Garcia ...
• How were the geologic time periods named? On what basis are they defined? Why is the use of living faunas acceptable for defining the periods and epochs of the Cenozoic Era? Make bar graph showing breakdown of the scale. Fossil...
• Pushdown Automaton (PDA) A Pushdown Automaton is a nondeterministic finite state automaton (NFA) that permits ε-transitions and a stack. Pushdown Automaton (PDA) PDA Example: The language, Lwwr, is the even-length palindromes over alphabet {0,1}.
• Created 2009 Evented I/O for JavaScript Server Side JavaScript Runs on Google's V8 JavaScript Engine Why Use Node.js ? Node's goal is to provide an easy way to build scalable network programs. What is unique about Node.js? JavaScript on server-side...
• Times New Roman Arial Arial Unicode MS Symbol Fireball 1_Fireball Microsoft Graph 2000 Chart Slide 1 Terminology Chain of Events for Direct Action Direct Action Chain of Events for Indirect Action Indirect Action Indirect Action (cont.) Stochastic (Random) Effects Linear...
• ERCOT Financial Summary For the Period Ending August 31, 2004 Board of Directors Meeting September 21, 2004 FY 2004 Results (Income Statement) 2004 Forecast 2004 Forecast Reasons for Lower Capital Spend in 2004 Reduced Scope by Market on Competitive Metering,...
• Eelc supplied = Q absorbed. VIt = mLv +Hlost. Challenge: One student puts his hand in a pot of boiling water at 100oC, a second places her hand into a container containing steam at 100oC. Who gets the worse burn?...
• Performing regression on noisy data can result in models that capture noise in addition to the underlying function. Preference for smoothness can be encoded in the regression problem by adding a regularization term to the objective function. where ?≥0 is...