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What I Have Learned
Great! You have reached this part of the module. To ensure your full
understanding on the concepts related to illustrating the need for axiomatic
structure of a mathematical system in general, and in Geometry it's important
that you are able to complete each statement below.
Activity 4: State Met
Illustrate the following properties by giving an example on each. Write your
answer on the space provided.
a. Reflexive Property of Equality
b. Symmetric Property of Equality
c. Transitive Property of Equality
d. Addition Property of Equality
e. Subtraction Property of Equality
​

Sagot :

brightwin19

Answer:

A.The reflexive property states that any real number, a, is equal to itself. That is, a = a. The symmetric property states that for any real numbers, a and b, if a = b then b = a. The transitive property states that for any real numbers, a, b, and c, if a = b and b = c, then a = c.

B.One way to remember the Symmetric Property of Equality is to think about the words symmetric or symmetrical. If you fold a piece of paper in half, and both halves have the exact same shape, then the piece of paper is symmetrical. Each half is the mirror image of the other half.

C.Here are some examples: If x=7 and 7=y, then x=y. If t=17 and 17=x+3, then t=x+3. If x+y=z+w and z+w=a+b, then x+y=a+b.

D.Expressions and Equations

 

An equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side. Expressions are made up of terms, and the number of terms in each expression in an equation may vary.

 

Algebraic equations contain variables, symbols that stand for an unknown quantity. Variables are often represented with letters, like x, y, or z. Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of 3x is 3.

 

 

Using the Addition Property of Equality

 

An important property of equations is one that states that you can add the same quantity to both sides of an equation and still maintain an equivalent equation. Sometimes people refer to this as keeping the equation “balanced”. If you think of an equation as being like a balance scale, the quantities on each side of the equation are equal, or balanced.

E.For all real numbers x,y, and z , if x=y , then x−z=y−z .

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