Question

In the given figure, parts of triangles indicated by identical marks are congruent.

a. Identify the one-to-one correspondence of vertices in which the two triangles are congruent and write the congruence.

b. State with reason, whether the statement, ∆XYZ \(\cong\) ∆STU is right or wrong.

Answer 1

a. From the figure, 

S ↔ X, T ↔ Z, U ↔ Y i.e., 

STU ↔ XZY, or SUT ↔ XYZ, or 

TUS ↔ ZYX, or TSU ↔ ZXY, or 

UTS ↔ YZX, or UST ↔ YXZ

∴ ∆STU \(\cong\) ∆XZY, or ∆SUT \(\cong\) ∆XYZ, or

∆TUS \(\cong\) ∆ZYX, or ∆TSU \(\cong\) ∆ZXY, or

 ∆UTS \(\cong\) ∆YZX, or ∆UST \(\cong\) ∆YXZ

b. If ∆XYZ \(\cong\) ∆STU, then 

∠Y \(\cong\) ∠T, ∠Z \(\cong\) ∠U,

seg XY \(\cong\) seg ST, seg XZ \(\cong\) seg SU 

∴ But, all the above statements are wrong. The statement AXYZ \(\cong\) ASTU is wrong.