Question

If \[\Delta {\text{DEF}} \cong \Delta {\text{BCA}}\],write part(s) of \[\Delta {\text{BCA}}\] that correspond to \[\angle {\text{E}}\]

Answer 1

Hint: Since \[\Delta {\text{DEF}} \cong \Delta {\text{BCA}}\], then each side and the angle of the first triangle will correspond to respective sides and angles of the other triangle. So we need to write the parts of
\[\Delta {\text{BCA}}\] which correspond to\[\angle {\text{E}}\].

Complete step by step solution:

We are given that \[\Delta {\text{DEF}} \cong \Delta {\text{BCA}}\]and we need to find the part(s) of \[\Delta {\text{BCA}}\] which correspond to\[\angle {\text{E}}\].
In congruent triangles each side of the first triangle is equal to the corresponding side of the second triangle.
Also each angle of the first triangle is equal to the corresponding angle of the second triangle.
Since \[\Delta {\text{DEF}} \cong \Delta {\text{BCA}}\]
Therefore,
The corresponding sides of \[\Delta {\text{DEF}}\]and \[\Delta {\text{BCA}}\] are equal:
\[
  {\text{DE = BC}} \\
  {\text{EF = CA}} \\
  {\text{FD = AB}} \\
 \]
The corresponding angles of \[\Delta {\text{DEF}}\]and \[\Delta {\text{BCA}}\] are equal:
\[
  \angle {\text{D = }}\angle {\text{B}} \\
  \angle {\text{E = }}\angle {\text{C}} \\
  \angle {\text{F = }}\angle {\text{A}} \\
 \]
Hence the \[\angle {\text{E}}\] of \[\Delta {\text{DEF}}\] corresponds to \[\angle {\text{C}}\]of \[\Delta {\text{BCA}}\].

Note:
Two triangles are congruent if and only if their corresponding sides or angles or both of two triangles are equal . They can be congruent by any one rule of congruence namely ASA, SAS, SSS or AAA.