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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. |
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Answer» 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] |
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