Class 8 MAHARASHTRA STATE TEXTBOOK BUREAU Solutions Maths Chapter 13: Congruence of triangles

(i)

In ∆ WXZ and ∆ WYZ 

WX ≅ WY Given

∠ XWZ ≅ ∠ YWZ Given

WZ ≅ WZ Common side

By Side-Angle-Side test ∆ WXZ and ∆ WYZ are congruent.

WXZ ↔ WYZ

(ii)

In ∆ KJI and ∆ LJI

KI ≅ LI Given

JI ≅ JI Common side and hypotenuse

∠ IJK ≅ ∠ IJL Each angle is 90˚

By hypotenuse side test  ∆ KJI and ∆ LJI are congruent

KJI ↔ LJI

(iii)

In ∆ EFG and ∆ EGH

EH ≅ GF Given

HG ≅ EF Given

EG ≅ EG Common side

By SSS test ∆ EFG and ∆ FGH are congruent

EFG ↔ GHE

(iv)

In ∆ SMA and ∆ TPO

∠ MSA ≅ ∠ POT Given

SM ≅ PO Given

∠ AMS ≅ ∠ OPT Given

By ASA test ∆ SMA and ∆ TPO are congruent.

SMA ↔ OPT

(v)

In ∆ TNS and ∆ TNM

TM ≅ TS Given

∠ MTN ≅ ∠ STN Given

∠ TMN ≅ ∠ TNS Given

By SAA test ∆ TNS and ∆ TNM are congruent

TNS ↔ TNM

(1)

In ∆ MBT and ∆ TBM

MS ≅ BT Given

∠ MST ≅ ∠ MBT Right angle

MT ≅ MT Common side

∆ MBT ≅ ∆ TBM by hypotenuse side test

Side ST ≅ side BM

∠ SMT ≅ ∠ BTM

∠ STM ≅ ∠ BMT

(2)

In ∆ PQR and ∆ TSR

QR ≅ SR Given

PR ≅ TR Given

∠ PRQ ≅∠ TRS Vertically opposite angles 

By SAS test ∆ PQR and ∆ TSR triangle are congruent

∆ PQR ≅ ∆ TSR 

Side PQ ≅ side TS

∠ RPQ ≅ ∠ RTS, ∠ PQR ≅ ∠ TSR

(3)

In ∆ HCD and ∆ FCD

DC ≅ DC Common side

∠ DHC ≅ ∠ DFC Given

∠ HCD ≅ ∠ FCD Given

By SAA test ∆ HCD ≅ ∆ FCD are congruent

Side HC ≅ side FC

∠ HDC ≅ ∠ FDC

Side HD ≅ side FD

In AAS test we need one side to be congruent and one angles on the line and other is opposite to the line.

Hence, either

∠ DAB = ∠ ECB and ∠ ABD = ∠ CBE 

OR 

∠ ADB = ∠ CEB and ∠ ABD = ∠ CBE