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 ≅ ∆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 ≅ ∆XZY, or ∆SUT ≅ ∆XYZ, or 

∆TUS ≅ ∆ZYX, or ∆TSU ≅ ∆ZXY, or 

∆UTS ≅ ∆YZX, or ∆UST ≅ ∆YXZ 

b. If ∆XYZ ≅ ∆STU, then 

∠Y ≅ ∠T, ∠Z ≅ ∠U, 

seg XY ≅ seg ST, seg XZ ≅ seg SU 

∴ But, all the above statements are wrong. 

The statement AXYZ ≅ ASTU is wrong.