In the given figure, parts of triangles indicated by identical marks a

1.	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» 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.

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»

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.