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Question

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.
(1)


(2) 

(3)


Solution

(1)


In ∆MST and ∆TBM,

side MS ≅ side TB (given)
∠MST ≅ ∠TBM (right angle)
side MT is common

∴ By Hypotenuse-side test, ∆MST ≅ ∆TBM.

∴ side ST ≅ side MB,
∠SMT ≅ ∠BTM,
∠STM ≅ ∠BMT.

(2) 


In ∆PRQ and ∆TRS,

side PR ≅ side RT (given)
side QR ≅ side RS (given)
∠PRQ ≅ ∠SRT (vertically opposite angles)

∴ By SAS test, ∆PRQ ≅ ∆TRS.
∴ side PQ ≅ side ST,
∠QPR ≅ ∠STR,
∠PQR ≅ ∠TSR.

(3)


In ∆DHC and ∆DFC,

∠DCH ≅ ∠DCF (given)
∠DHC ≅ ∠DFC (given)
side DC is common

∴ By AAS test, ∆DHC ≅ ∆DFC.
∴ side DH ≅ side DF,
side HC ≅ side FC,
∠HDC ≅ ∠FDC.

Mathematics
Mathematics - Solutions
Standard VIII

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