Question

state the test and one correspondence of vertices by which pair triangle is cogurent​

Answer 1

Question

1. In each pair of triangles given below, parts shown by identical marks are congruent. State the test and the one to one correspondence of vertices by which triangles in each pair are congruent and remaining congruent parts.

Answer

(1)

In ∆MST and ∆TBM, we have

side MS ≅ side TB …. (given)

∠MST ≅ ∠TBM …. (right angle)

And, side MT is common

Hence, by Hypotenuse-side test ∆MST ≅ ∆TBM.

Now, from corresponding parts of congruent triangles

side ST ≅ side MB,

∠SMT ≅ ∠BTM,

∠STM ≅ ∠BMT.

(2)

In ∆PRQ and ∆TRS, we have

side PR ≅ side RT …. (given)

side QR ≅ side RS …. (given)

∠PRQ ≅ ∠SRT …. (vertically opposite angles)

Hence, by SAS test ∆PRQ ≅ ∆TRS.

Now, from corresponding parts of congruent triangles

side PQ ≅ side ST,

∠QPR ≅ ∠STR,

∠PQR ≅ ∠TSR.

(3)

In ∆DHC and ∆DFC, we have

∠DCH ≅ ∠DCF …. (given)

∠DHC ≅ ∠DFC …. (given)

And, side DC is common

Hence, by AAS test ∆DHC ≅ ∆DFC.

Now, from corresponding parts of congruent triangles

side DH ≅ side DF,

side HC ≅ side FC,

∠HDC ≅ ∠FDC.