2 Marks Questions

Question 12 Marks

In two triangles ABC and DEF, it is given that $\angle\text{A}=\angle\text{D},\angle\text{B}=\angle\text{E}$ and $\angle\text{C}=\angle\text{F},$ Are the two triangles necessarily congruent?

Answer

It is given that $\angle\text{A}=\angle\text{D},\angle\text{B}=\angle\text{E},\angle\text{C}=\angle\text{F}$

For necessarily trialnge to be congruent, sides also be equal.

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Question 22 Marks

In Fig. it is given that $\text{AB}=\text{CD}$ and $\text{AD}=\text{BC}.$ Prove that $\triangle\text{ADC}\cong\triangle\text{CBA}.$

Answer

In $\triangle\text{ADC}$ and $\triangle\text{CBA}$ $\text{AB}=\text{CD}$ (given) $\text{AC}=\text{AC}$ (common) $\text{AD}=\text{BC}$ (given) By SSS congurence criterion $\triangle\text{ADC}\cong\triangle\text{CBA}$

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Question 32 Marks

In a $\triangle\text{PQR,}$ if $\text{PQ}=\text{QR}$ and L, M and N are the mid-points of the sides $PQ, QR$ and $RP$ respectively. Prove that $\text{LN}=\text{MN}.$

Answer

$\frac{1}{2}\text{PQ}=\frac{1}{2}\text{QR}$
$\Rightarrow\text{PL}=\text{MR}$
$\text{PN}=\text{NR}$
$(\because$ N is themid-point of $PR)$
$\angle\text{LPN}=\angle\text{MRN}$
$(\because\text{QP}=\text{QR})$
$\therefore$ From SAS $\triangle\text{PNL}\cong \triangle\text{RNM}$
$\therefore\text{LN}=\text{NM}$ (c.p.c.t)

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