Cumulative Standards Review
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Write all the corresponding congruent parts of the two triangles and compare them to each statement.
H
Here we are told that "∠ A and ∠ J are vertical angles," which implies that ∠ A≅ ∠ J. Notice that this does not contradict any of the congruence statements written above. In fact, it is one of them!
Now we have "BC is the hypotenuse of △ ABC." Again, this statement does not contradict the fact that △ ABC ≅ △ JMK. This only tells us that both triangles are right triangles.
The statement "△ ABC is isosceles and △ JMK is scalene" contradicts the fact that △ ABC ≅ △ JMK. Let's see why.
If △ ABC is isosceles then it must have two sides with the same length. Let's suppose that AB≅ BC. Then, we can rewrite the relations given above as follows. AB &≅ JM AB &≅ MK Then, by the transitivity property of ≅, we get that JM≅ MK. But wait a minute! This is not possible because △ JMK is scalene, which means that all three sides have different lengths.
Finally, we are told that "AB is not congruent to MK." Notice that this does not contradict any of the congruence relations written above.
The only option which contradicts the congruence relations is option H. Therefore, it is the correct answer.