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 ≅ ∆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 ≅ ∆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.

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»

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.