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Page No 85:

Question 1:

In each pair of triangles in the following figures, parts bearing indentical marks are congruent. State the test and correspondence of vertices by which triangles en each pair are congruent.
(i) 

(ii)

 

(iii) 

(iv)



(v)

Answer:

(i)


By SAS test, in the correspondence XWZ ↔ YWZ.

(ii)

 

By Hypotenuse-side test, in the correspondence KJI ↔ LJI.

(iii) 


By SSS test, in the correspondence HEG ↔ FGE.

(iv)



By ASA test, in the correspondence SMA ↔ OPT.

(v)


By SAA test, in the correspondence MTN ↔ STN.



Page No 87:

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.
(1)


(2) 

(3)

Answer:

(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.

Page No 87:

Question 2:

In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test ?

Answer:

In ∆ABD and ∆EBC,

side AD ≅ side EC (given)
∠ABD ≅ ∠EBC (vertically opposite angles)

∴ To show that ∆ ABD and ∆ EBC will be congruent by A-A-S test, one of the following is needed:
∠BAD ≅ ∠BCE
or
∠BDA ≅ ∠BEC.



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