Which triangles are similar?
justify your reasoning

Triangles OPQ and NPR are similar by AA Similarity Postulate

Step-by-step explanation:

we know that

In this problem

NR is parallel to OQ

therefore

Triangles OPQ and NPR are similar by AA Similarity Postulate (the three internal angles are congruent)

because

<RNP=<QOP -----> by corresponding angles

<NRP=<OQP ----> by corresponding angles

<NPR=<OPQ

Remember that

If two triangle are similar, then the ratio of its corresponding sides is equal

Verify

substitute the values

-----> is true

therefore

The triangles OPQ and NPR are similar

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

13

step-by-step explanation:

divide the cost of the total of sodas you bought by the cost of one soda, for example:

$24.57 divided by $1.89 is 13 which means you bought 13 sodas