Question

In two or more complete sentences, explain what additional information is needed to prove triangle CES congruent to triangle RST.
please help im confused

Answer 1

We already know that angles ECS and TRS are congruent, because they are both right angles (given). We also know that angles CSE and RST are congruent because they are vertical angles and vertical angles are always congruent. That gives us two sets of congruent angles. We just need to know something about one pair of sides to prove the two triangles congruent to each other. I do question the order of the letters in the names of the triangles--if that's really the order the letters are written in the problem, then we would need to know that ES is congruent to RT or that CS is congruent to ST. If the order of the letters of the names of the triangles is a little different we would need to know that CS is congruent to RS or that any of the other sides that appear to match are actually congruent. 

Answer 2

To prove that triangle CES is congruent to RST, we can determine it through the following comparisons: (1) SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. (2) SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.