Match the following statements to the reasons listed.

note: in a traditional proof format, the statements would be on the left side of the proof.

given:
rm = sn
tm = tn
prove:
rn = sm

1. rm = sn, tm = tn addition property of equality
2. ∠t = ∠t reflexive
3. rm + tm = sn + tn substitution
4. rm + tm = rt, sn + tn = st betweeness
5. rt = st cpcte
6. triangle rtn congruent to triangle stm given
7. rn = sm sas

We have to match the following statements to the given proof.

S.No.            Proof                                                     Statement

 1                 RM=SN                                                    Given

                    TM=TN

  2                ∠T=∠T                                                    Reflexive

  3                 RM+TM=SN+TN                            Addition property

                                                                                    of equality

                                                                                     ( by using 1)

   4                 RM+TM=RT,                                    Betweeness

                       SN+TN=ST                

   5                  RT=ST                                        Substitution( since using                                              

                                                                            equation 3 and 4)  

    6              ΔRTN≅ΔSTM                               SAS ( since two sides and

                                                                           corresponding angle are

                                                                             equal by 1,2 and 5)

     7                RN=SM                                    CPCTE( Corresponding parts of

                                                                         congruent triangles are equal)

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional