Question

Triangle ABC is similar to triangle CDE. Both are right triangles. Which statements about the two triangles must be true? Choose all answers that are correct. A. Sides AB and BC are proportional to sides CD and DE. B. Side AC has the same slope as side CE. C. Triangle ABC is congruent to triangle CDE. D. Side AC is congruent to side CE.

Answer 1

In similar right triangles, the corresponding sides are proportional. The slope of a side is not necessarily the same as the slope of a corresponding side in similar triangles. Triangular congruence occurs when the corresponding sides and angles of two triangles are equal.

Step-by-step explanation:

In similar right triangles, the corresponding sides are proportional. Therefore, statement A is correct: sides AB and BC are proportional to sides CD and DE.

However, the slope of a side is not necessarily the same as the slope of a corresponding side in similar triangles. Therefore, statement B is incorrect: side AC does not have the same slope as side CE.

Triangular congruence occurs when the corresponding sides and angles of two triangles are equal. Since we only know that the sides are proportional and not equal, statement C is incorrect: triangle ABC is not congruent to triangle CDE.

Lastly, congruent triangles have all corresponding sides equal in length. Since we only know that the sides are proportional and not equal, statement D is incorrect: side AC is not congruent to side CE.

Answer 2

The question ask to choose among the choices that states the truth about the triangle ABC and triangle CDE which is they are similar. The statement that tells the truth is letter C. Triangle ABC is congruent to triangle CDW and also D. Side AC is congruent it side CE. I hope this will help