Geometry Properties Questions! Trivia Quiz

Explanation
The given equation "a=a" is an example of a reflexive relation. A relation is reflexive if every element is related to itself. In this case, "a" is related to itself because it is equal to itself. Therefore, the answer is reflexive.

Explanation
The given statement "If 5=x, then x=5" is an example of a symmetric statement. This is because the statement remains true regardless of the order in which the variables are presented. In this case, whether we say "5=x" or "x=5", the meaning remains the same and the statement holds true. Therefore, the answer is symmetric.

Explanation
The given statement "If a=b and b=c, then a=c" is an example of the transitive property. The transitive property states that if two things are equal to a third thing, then they are also equal to each other. In this case, if a is equal to b and b is equal to c, then it follows that a is also equal to c. This property is commonly used in mathematics and logic to establish relationships and make deductions based on given information.

Explanation
The given statement is a basic property of addition, which states that if two numbers are equal (a=b), then adding the same number to both sides of the equation will still result in equality (a+c=b+c). This property is commonly used in algebraic manipulations and helps to simplify equations.

Explanation
The given statement is a mathematical equation that states that if a equals b, then subtracting the same value c from both a and b will still result in them being equal. This property is known as the subtraction property of equality, where subtracting the same value from both sides of an equation does not change the equality. Therefore, the correct answer is subtraction, which refers to the operation of subtracting a value from both sides of an equation.

Explanation
The given statement is a mathematical property that states if two numbers are equal (a=b), then multiplying both sides of the equation by the same number (c) will still result in equality (a*c=b*c). This property holds true for any real numbers and is a fundamental concept in algebra.

Explanation
The given statement states that if a is equal to b and c is not equal to 0, then the division of a by c is equal to the division of b by c. This is a basic property of division, where if two numbers are equal and divided by the same non-zero number, their results will also be equal. Therefore, the correct answer is division.

Explanation
The given equation "a+b = b+a" represents the commutative property of addition. This property states that the order of the numbers being added does not affect the sum. In other words, when adding two numbers, it doesn't matter which number comes first, the result will always be the same. This property holds true for all real numbers and is a fundamental property of addition.

Explanation
The given statement "ab = ba" implies that the order of multiplication does not matter. This property is known as commutativity, specifically for multiplication. In mathematics, if a binary operation (such as multiplication) is commutative, it means that the order of the operands does not affect the result. So, the correct answer is "commutative for multiplication."

Explanation
The given correct answer states that "(a+b)+c = a+(b+c)" is an example of the associative property for addition. This property states that the grouping of numbers being added does not affect the sum. In this case, regardless of whether we add (a+b) first and then add c, or add a and then add (b+c), the final sum will be the same. Therefore, the equation satisfies the associative property for addition.

Explanation
The given correct answer states that (ab)c is equal to a(bc), which is the associative property for multiplication. This property states that when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, it doesn't matter if we first multiply a and b and then multiply the result by c, or if we first multiply b and c and then multiply the result by a. The answer correctly identifies this property as the associative property for multiplication.

Explanation
The given equation "a+0=a" represents the identity for addition. This means that when any number "a" is added to zero, the result will always be the same number "a". This property holds true for all real numbers. The term "identity for addition" refers to the fact that adding zero to any number does not change its value. However, there seems to be a typo in the word "identity" as "identitly" in the question.

Explanation
The given correct answer is "identity for multiplication". This is because the equation 1a=a represents the property of an identity element in multiplication, where any number multiplied by 1 gives the same number as the product. The term "Identitly for multiplication" appears to be a typographical error and does not provide a valid explanation.

Explanation
The given equation states that when a number "a" is added to its inverse "-a", the result is always zero. This is because the inverse for addition is the opposite of a number that, when added to the original number, yields zero. Therefore, the equation a + (-a) = 0 holds true.

Explanation
The given equation states that when a number is multiplied by its reciprocal, the result is always 1. This property is known as the inverse for multiplication. It means that any non-zero number, when multiplied by its reciprocal, will always yield the multiplicative identity, which is 1. Therefore, the correct answer is "inverse for multiplication".

Explanation
The given statement states that if two variables, a and b, are equal to each other, then it is possible to replace the variable a with the variable b. This process is known as substitution, where one variable is substituted with another that has the same value. In this context, the correct answer is substitution as it accurately describes the process explained in the statement.