Question

In the adjacent figure, parts of triangles indicated by identical marks are congruent
(i) Identify the one to one correspondence of vertices in which the two triangles are congruent and write the congruence in two ways.
(ii) State with reason, whether the statement, Δ XYZ ≡ Δ STU is right or wrong.

Answer 1

Thanking you for the above question ;

According to the above picture ,

XY = SU

YZ = UT

XZ = ST .

So point congruence is for the following groups ( X , S ) , ( Y , U ) , ( T , Z )

∠ T = ∠ Z
∠U = ∠ Y
∠ X = ∠S

We see that We got all corresponding parts of two triangles to be equal .

So ,
By Any of the Axioms SSS , ASA , SAS

The above triangles are congruent .

We can write congruence in many ways. I am writing three of them below


ΔXYZ ≅ ΔSUT

ΔXZY≅ ΔSTY

ΔYZX ≅ ΔUTS

2) Δ XYZ ≡ Δ STU This statement is wrong .

According to this ,

XY = ST , YZ = TU , ZX = US , But this contradicts the above relation .

So , Δ XYZ ≡ Δ STU is wrong

Answer 2

Hi ,

From the figure given ,

In triangle SUT and triangle XYZ

SU = XY ( side )

UT = YZ ( side )

TS = ZX ( side )

Therefore ,

triangle SUT conguent to triangle XYZ

( sss congruency )

2 )

<S = <X ( angle )

<U = <Y ( angle )

<T = <Z ( angle )

Therefore ,

Triangle SUT is congruent to Triangle XYZ

( AAA congruency )

3 ) In Triangle XYZ and Triangle STU

XY is not equal to ST

( corresponding parts of the triangles are not

equal )

Triangle XYZ is not congruent to Triangle STU

I hope this helps you.

: )