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How do you find a counterexample?
When identifying a counterexample,
- Identify the condition and conclusion of the statement.
- Eliminate choices that don’t satisfy the statement’s condition.
- For the remaining choices, counterexamples are those where the statement’s conclusion isn’t true.
What’s an example of a counterexample?
An example that disproves a statement (shows that it is false). Example: the statement “all dogs are hairy” can be proved false by finding just one hairless dog (the counterexample) like below.
What is the correct congruence statement?
If two angle in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent. If in triangles ABC and DEF, angle A = angle D, angle B = angle E, and AB = DE, then triangle ABC is congruent to triangle DEF.
How do you disprove a counterexample?
A counterexample disproves a statement by giving a situation where the statement is false; in proof by contradiction, you prove a statement by assuming its negation and obtaining a contradiction.
What is a counterexample What are counterexample used for?
A counterexample is a special kind of example that disproves a statement or proposition. Counterexamples are often used in math to prove the boundaries of possible theorems. Counterexamples are helpful because they make it easier for mathematicians to quickly show that certain conjectures, or ideas, are false.
What is a congruence statement example?
A triangle with three sides that are each equal in length to those of another triangle, for example, are congruent. This statement can be abbreviated as SSS. If two triangles have two equal angles and a side of equal length, either ASA or AAS, they will be congruent.
What are the six congruence statements?
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
- SSS (side, side, side) SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.
- SAS (side, angle, side)
- ASA (angle, side, angle)
- AAS (angle, angle, side)
- HL (hypotenuse, leg)