Answer:
The complete question is shown below:
Step-by-step explanation:
The triangle and the menus with the statements to complete are missing.
From a similar question, the statments are:
Levi drew the triangle shown. He wants to draw a second triangle that is different from this one.
It is ____for Levi to draw a second triangle with different angle measures and the same side lengths.
It is____for Levi to draw a second triangle with different side lengths and the same angle measures.
Solution
As for the first statement, the word to fill in the blank is impossible.
It is impossible for Levi to draw a second triangle with different angle measures and the same side lengths.
If the three sides of a triangle are equal to the three sides of other triangle, then they are equal, and the angle measures are also equal.
Thus, if the second triangle has different angle measures it cannot have the same side lengths.
You can base your answer on the postulate named SSS: if three sides of a triangle are congruent to the three sides of other triangle, then the triangles are congruent.
As for the second statement, the word that complete the statement is possible.
It is possible for Levi to draw a second triangle with different side lengths and the same angle measures.
Two triangles may have same angle measures and different side lenghts. having the same angle measures make them similar, by the Angle-Angle similarity postulate. If two angles of any two triangles are congruent, the third angles are also congruent, and thus the two triangles are similar. But the side lengths can be different, which make the triangles different.