___(0-10 pts) Describe the segment and angle properties of equality. Give at least 3 examples.

 

Properties of Equality
Addition property of Equality	If a = b, then a + c = b + c
Subtraction Property of Equality	If a = b, then a – c = b – c
Multiplication Property of Equality	If a = b, then ac= bc
Division Property of Equality	If a = b and c =/= 0, then a/c = b/c
Reflexive Property of Equality	a = a
Symmetric Property of Equality	If a = b, then b = a
Transitive Property of Equality	If a = b and b = c, then a = c
Substitution Property of Equality	If a = b and b = c, then a= c
Distributive Property	a(b + c) = ab + ac

 

 

 

                        

 

 

 

By: Ari Min Han :D

 

The segment Property of Equality, is used on the 2-column chart too. It is used to proof the segment, but depends on what the problem wants you to proof.

 

ADDITION PROPERTY: If a = b , then a + c = b + c .

SUBTRACTION PROPERTY: If a = b , then a - c = b - c .

MULTIPLICATION PROPERTY: If a = b , then ac = bc .

DIVISION PROPERTY: If a = b and c doesn’t= 0, then a / c = b /  c.

REFLEXIVE PROPERTY: For   a = a .

SYMMETRIC PROPERTY: If a = b , then b = a .

TRANSITIVE PROPERTY: If a = b and b = c , then a = c .

SUBSTITUTION PROPERTY: If a = b , then a can be substituted for b in any expression.

 

EXAMPLES~~~~~>

 

1)                                       Given

KM= KL + LM                  Segment Addition Postulate

5x-4= x+5 + 2x-1           Substitution P. of =

5x-4= 3x+4                     Simplify

2x-4=4                             Subtraction P. of =

2x=8                                 Addition P. of =

x=4                                   Divisoin P. of =

 

 

 

 

2)                                        Given

RS+ST= RT                        Segment Addition Postulate

5n+ 30 = 9n - 5                Substitution P. of =

30= 4n - 5                         Simplify

35= 4n                               Addition P. of =

8.75=n                               Division P. of =

 

 

 

3)                                             Given

AB=BC                                    Segment Addition Postulate

4x+6= 3x +15                       Substitution P. of =

x+6=15                                  Subtraction P. of =

x=9                                         Subtraction P. of =

 

 

 

 

 

_(0-10 pts) Describe how to write a two-column proof. Give at least 3 examples.

 

 

A two column proof is a proof in which has to be written using two-columns, obviously. In one column you have to have a statement and in the other column you have to have a reason. This is the structure you use in order to do a 2 column proof.

 

• What I mean by information given, is that they will give you a "given" statement and a "prove" statement.
• Given is what you are starting with and what your first statement be. Prove is what you have to prove throughout the proof, this should be the last part of the 2 column-proof.

 

 

1. Statement: Is the problem you conclude from the proof. Is what you have to give a name to. It's the what part of the proof.
2.  Reason: Is the theorem or postulate you give in order to give a name for the statement. It's the why part of the proof.

 

  You wirte a 2 column-proof by drawing 2 columns. The first column with a statement and the other with a reason. This is the structure you have to follow in order to draw a nice 2 column proof. You have to name the theorems and the postulates to give a reason.

 

    EXAMPLES:

 

 

1.)

 

Given: <1 congr. <4

Prove: <2 congr. <3

 

  Statements:                                                    Reason:

1. <1 congr. <4                                            1. Given

2. <1 congr. <2 and <3 congr. <4              2. Vert. <s theorem.

3. <2 congr. <4                                            3. Transitive. Property of congr. 

4. <2 congr. <3                                            4. Transitive. Property of congr. 

 

        

2.)

 

Given: <LXN is a right angle

Prove: <1 and <2 are complementary

 

   Statement:                                                            Reason:

1. <LXN= 90 degrees                                             1. Given

2. m<LXN=90                                                         2. Def. of right angles

3. m<1 + m<2=m<LXN                                         3. Angle Addition Postulate. (AAP)

4.) m<1 + m<2=90                                                4. Substitution

5. <1 and <2= complementary                              5. definition of complementary

 

 

3.)

 

Given: BD bisects

Prove: 2m<1 = m<ABC

 

           Statement:                                          Reason:

1. BD bisects <ABC                                     1. Given

2. <1 cong. <2                                            2. Def. Bisect

3. m<1+m<2=m<ABC                               3. Angle Addition Bisects

4. m<1 cong. m<2                                     4. Def. of Congruent

5. m<1 + m<1= m<ABC                           5. Substitution

6. 2m<1=m<ABC                                       6. Simplify

6. 2 m<1 = m<ABC                            

 

                                                                                                             Javier Garcia 10-1                

 

Examples:

 

1)

Given : <1 and <2 from a linear pair

Prove: <1 and <2 are supplementary

 

1. <1 and <2 form a linear pair.                      1. Given

2. -> BA and -> BC form a line.                       2. Def. of. linear pair

3. m<ABC = 180*                                              3. Def. of straight angle

4. m<AB + m<BC = m<ABC                            4. Angle addition postulate

5. <1 + <2 = 180*                                             5. Substitution 

6. <1 and <2 are supplementary                     6. Def. of supplementary

 

 

2)

Given: m<LAN = 30*, m<1 = 15*

Prove: -> AM bisects <LAN

 

1) m<LAN = 30*, m<1 = 15*                               1. Given

2) m<1 + m<2 = m<LAN                                    2. Angle addition postulate

3) m<1 + m<2 = 30*, 15* + m<2 = 30*            3. Substitution

4) m<2 = 15*                                                         4. Subtraction

5) m<2 = m<1                                                      5. Transitive

6) m<2 =~ m<1                                                   6. Def. of Congruence

7) AM bisects <LAN                                             7. Def. of bisect

 

3)

Given: <2 =~ <3 

Prove: <1 and <3 are supplementary

 

1) <2 =~ <3                                                         1. Given

2) m<2 = m<3                                                     2. Congruent supp. theorem

3) <1 and <2 form a linear pair                         3. Linear pair theorem

4) m<1 + m<2 = 180*                                        4. Def. of a supp. anlge

5) m<1 + m<3 = 180*                                        5. Def. of. supplementary

6) <1 and <3 are supplementary                      6. Def. of. supplementary

 

Nicolas Busto 10-4