Question

Triangle ABC is similar to triangle CDE. Both are right triangles.

Answer 1

Let's review "similar" and "congruent."  "Congruent" means the same--so two congruent line segments will be the same length; two congruent figures have the same angle measures, same side lengths, same area, etc.  "Similar" means that the sides and area are PROPORTIONAL, not the same: you can divide or multiply them all by the same number and get the measures of the other.  Note that the angles must still be the same measures.

So, let's look at A, first comparing AB and CD.  AB is 4 units long, and CD is 2 units long.  4/2=2, so AB is twice the length of CD.  What about BC and DE?  BC=6, and DE=3.  6/3=2.  Since BOTH AB and BC are twice the length of CD and DE, they are proportional.  A is correct!

In B, if side AC has the same slope as side CE, then basically they have the same incline.  They are on the same line, and this line has a slope.  Since they are both on this line, they both must have the same slope as this line, and therefore the same slope as each other.  B is correct.

What about C?  Are the triangles congruent?  NO, because their side lengths are different (though proportional).  C is incorrect.  And D?  Just looking at the diagram, we can tell that AC is not the same length as DE, so they are NOT congruent (though again, they are proportional).  D is incorrect.

Answer: A, B