Question

Which choice is a correct congruence statement for the triangles?

Answer 1

Answer: Choice 3)  Triangle ACB = Triangle CAD

The reason why is because the order is important when it comes to congruent statements. I'm referring to the order of the letters of ACB and CAD.

Each answer choice has "ACB" in that exact order shown on the left hand side of each congruent statement. We have "A" listed first, then "C" next. In short, segment AC is the first thing mentioned of ACB. This means that we need to list out segment AC as the first thing for the other triangle as well, in order to have a match. Segment AC is the same as segment CA, which is the first segment mentioned in triangle CAD. That's why choice 3 is the answer.

Note how something like triangle CDA won't work since segment CD is listed first, which doesn't pair up with segment AC. This allows us to rule out the first answer choice. Choices 2 and 4 can be eliminated for similar reasons.

Put another way: let's assume choice 1 was the answer. That would mean that AC = CD as they are the first pair of letters of ACB and CDA respectively. But the diagram shows that AC = CD is not true; otherwise, the segments would have similar tickmarks to show they are the same length. This is an alternative way to see why choices 1, 2, and 4 can be crossed off the list.