Question

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

i.

Answer 1

i. In ∆MST and ∆TBM, 

∴ side MS ≅ side TB … [Given] 

m∠MST = m∠TBM = 90° … [Given] 

hypotenuse MT ≅ hypotenuse MT

…[Common side] 

∴ ∆MST ≅ ∆TBM …[by hypotenuse-side test] 

∴ side ST ≅ side BM …[Corresponding sides of congruent triangles] 

∠SMT ≅ ∠BTM …[Corresponding sides of congruent triangles] 

∠STM ≅ ∠BMT …[Corresponding sides of congruent triangles] 

ii. In ∆PRQ and ∆TRS, side PR ≅ side TR … [Given] 

∠PRQ ≅ ∠TRS …[Vertically opposite angles] 

side RQ ≅ side RS … [Given] 

∴ ∆PRQ ≅ ∆TRS …[by SAS test] 

∴ side PQ ≅ side TS …[Corresponding sides of congruent triangles] 

∠RPQ ≅ ∠RTS …[Corresponding sides of congruent triangles]

∠PQR ≅ ∠TSR …[Corresponding sides of congruent triangles] 

iii. In ∆DCH and ∆DCF,

∠DCH ≅ ∠DCF …[Given] 

∠DHC ≅ ∠DFC …[Given] 

side DC ≅ side DC …[Common side] 

∴ ∆DCH ≅ ∆DCF …[by AAS test] 

∴ side HC ≅ side FC …[Corresponding sides of congruent triangles] 

side DH ≅ side DF…[Corresponding sides of congruent triangles] 

∠HDC ≅ ∠FDC ….[Corresponding sides of congruent triangles]