Triangle xyz has been dilated to form triangle lmn. what is the least amount of information needed to prove the two triangles are similar?
a. two pairs of corresponding angles and one pair of corresponding sides.
b. two pairs of corresponding sides and one pair of corresponding angles.
c. two pairs of corresponding angles.
d. two pairs of corresponding sides.

C.Two pairs of corresponding angles.

Step-by-step explanation:

Given that Triangle XYZ has been dilated to form triangle LMN.

For two triangles to be similar we must have either corresponding angles are congruent or corresponding sides are similar

When we are given two angles are equal, third angle would be 180 -(sum of two angles) would automatically be congruent.

Hence correct answer would be

C.Two pairs of corresponding angles.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: