Vertical angles must necessarily be congruent, however congruent angles do not necessarily have to be vertical angles.
An example of congruent angles which are not vertical angles are the 3 interior angles of an equilateral triangle. These angles do not share the same vertex yet they are congruent.
Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.
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Counter Example
If the conditional (if, then) is true, then the contrapositive (reversed; if not, then not) will be also true. And vice versa, if the conditional is false, its contrapositive will be also false. for example,If a graph passes the vertical line test, then it is a graph of a function. (True)If a graph is not a graph of a function, then it will not pass the vertical line test. (True)Yes, but only if the original if-then was true.
Learn the definitions. Any angle greater than 90º is obtuse. Two angles are congruent if and only if they are equal. For example, 105º ≠ 150º, but both are greater than 90º; therefore, they are not congruent. Obtuse, fersure!
Counter-example
You figure it out!
Only some statements have both examples and counter examples. A sufficiently clear and unambiguous statement would not have counter examples.
A counter example is a statement that shows conjecture is false.
counter example
It means that the person writing the statement does not fully understand what "regular" means.A polygon is regular if, and only if, all its sides are congruent andall its angles are congruent.A rhombus, for example, has all its sides congruent but a rhombus is not a regular quadrilateral.It means that the person writing the statement does not fully understand what "regular" means.A polygon is regular if, and only if, all its sides are congruent andall its angles are congruent.A rhombus, for example, has all its sides congruent but a rhombus is not a regular quadrilateral.It means that the person writing the statement does not fully understand what "regular" means.A polygon is regular if, and only if, all its sides are congruent andall its angles are congruent.A rhombus, for example, has all its sides congruent but a rhombus is not a regular quadrilateral.It means that the person writing the statement does not fully understand what "regular" means.A polygon is regular if, and only if, all its sides are congruent andall its angles are congruent.A rhombus, for example, has all its sides congruent but a rhombus is not a regular quadrilateral.
A counter example is a proof of a negation of a universal statement.A statement of the form "all X are Y" (e.g. all men are mortal), can be disproved by providing a counter example (here: something (someone) which is both a man and immortal).A more mathematical example of the use of a counter example could be to disprove the statement "the product of two prime numbers is odd". This is a claim about all numbers which are the product of two prime numbers (all elements in the set {n in N | n = p*q where p and q are prime numbers}). This set contains infinitely many pair numbers, but a single example (or witness), is enough to disprove the statement. Four is such a number and can serve as a counter example.
to find a counterexample
Congruent angles are of the same size as for example 85 degrees is congruent to 85 degrees
A rectangle with dimensions of 1" x 2" .
The lengths of the sides need not be congruent. For example, consider a square and a rectangle.
Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.