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Question 11 Mark

Is it possible to construct a triangle with lengths of its sides as $8\ cm, 7\ cm$ and $4\ cm?$ Give reason for your answer.

Answer

Yes, it is possible to construct a triangle with lengths of sides as $8\ cm, 7\ cm$ and $4\ cm$ as sum of any two sides of a triangle is greater than the third side.

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Question 21 Mark

It is given thet $\triangle\text{PQR}\cong\triangle\text{EDF},$ then Is it true to say that $PR = EF?$ Given reason for your answer.

Answer

Yes, $PR = FE$ becouse thry are the correponding sides of $\triangle\text{PQR}$ and $\triangle\text{EDF}.$

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Question 31 Mark

It is given thet $\triangle\text{ABC}\cong\triangle\text{RPQ}.$ Is it true to say thet $BC = QR?$ Why$?$

Answer

It is False that $BC = QR$ becouse $BC = PQ$ as $\triangle\text{ABC}\cong\triangle\text{RPQ}.$

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Question 41 Mark

Is it possible to construct a triangle with lengths of its sides as $9\ cm, 7\ cm$ and $17\ cm?$ Give reason for your answer.

Answer

No, it is not possible to construct a triangle whose sides are $9\ cm, 7\ cm$ and $17\ cm.$ Because, $9\ cm + 7\ cm = 16\ cm < 17\ cm.$ Whereas sum of any two sides of a triangle is always greater than the third side.

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Question 51 Mark

In $\triangle\text{ABC}$ and $\triangle\text{PQR},\angle\text{A}=\angle\text{Q}$ and $\angle\text{B}=\angle\text{R}.$ Which side of $\triangle\text{PQR}$ should be equal to side $AB$ of $\triangle\text{ABC},$ so that the two triangles are congruent? Give reason for your answer.

Answer

In triangle $ABC$ and $PQR,$
we have $\angle\text{A}=\angle\text{Q}$
$\angle\text{B}=\angle\text{R}$ For the triangle to be congruent,
we must $AB = QR.$ They will be congruent by $ASA$ rule.
$ BC = RP$ They will be congruent by $AAS$ congruence rule.

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