[4 marks sum]

Question 14 Marks

In the given figure, we have $P Q=S R$ and $P R=S Q$.
Prove that :
(i) $\triangle PQR \cong \triangle SRQ$
(ii) $\angle PQR =\angle SRQ$

Answer

self

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Question 24 Marks

In the given figure, $P L \perp O A$ and $P M \perp O B$ such that $O L=O M$.
Prove that :
(i) $\triangle OLP \equiv \triangle OMP$
(ii) $PL = PM$
(iii) $\angle LOP =\angle MOP$

Answer

self

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Question 34 Marks

In the given figure, $A B \perp B D, C D \perp B D$ and $A B=C D$.
Prove that :
(i) $\triangle ABD \equiv \triangle CDB$
(ii) $AD = CB$

Answer

self

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Question 44 Marks

In the given figure, we have $A O=B O$ and $C O=D O$.
Prove that :
(i) $\triangle AOC \cong \triangle BOD$
(ii) $AC = BD$

Answer

self

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Question 54 Marks

In the given figure, $\angle S P R=\angle Q R P$ and $\angle R S P=\angle P Q R$.
Prove that :
(i) $PQ = RS$
(ii) $PS = QR$

Answer

self

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Question 64 Marks

In the given figure, AB = CD and AD = CB.
Prove that :
(i) $\triangle ABD =\triangle CDB$
(ii) $\angle A =\angle C$

Answer

self

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Question 74 Marks

State, giving reason, whether the pair of triangle are congruent or not : $\triangle KLM$ in which $KM =4 cm, \angle K =75^{\circ}, \angle M =40^{\circ}$ and $\triangle PQR$ in which $PR =4 cm$, $\angle Q =65^{\circ}, \angle R =40^{\circ}$.

Answer

Yes, (ASA)

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Question 84 Marks

State, giving reason, whether the pair of triangle are congruent or not : $\triangle DEF$ in which $\angle E =48^{\circ}, DE =6 cm, EF =8 cm$ and $\triangle MNR$ in which $\angle R =48^{\circ}$, $MN =6 cm, MR =8 cm$.

Answer

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Question 94 Marks

State, giving reason, whether the pair of triangle are congruent or not : $\triangle ABC$ in which $\angle A =50^{\circ}, \angle B =60^{\circ}, BC =4.5 cm$ and $\triangle DEF$ in which $\angle E =60^{\circ}$, $EF =4.5 cm, \angle F =70^{\circ}$.

Answer

Yes, (AAS)
[Hint: $\angle C =180^{\circ}-(\angle A +\angle B )=70^{\circ}$ ]

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Question 104 Marks

State, giving reason, whether the pair of triangle are congruent or not : $\triangle ABC$ in which $AB =3 cm, \angle A =90^{\circ}, BC =5 cm$ and $\triangle KLM$ in which $KM =3 cm$, $\angle K =90^{\circ} cm , LM =5 cm$.

Answer

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Question 114 Marks

In the adjoining figure, $\triangle A B C$ is an isosceles triangle in which $A B=A C$. If $B M \perp A C$ and $C N \perp A B$,
prove that :
(i) $\triangle BMC \cong \triangle CNB$
(ii) $BM = CN$

Answer

$[$ Hint : $AB = AC \Rightarrow \angle ACB =\angle ABC ]$

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Question 124 Marks

In the adjoining figure, $\triangle A B C$ is an isosceles triangle in which $A B=A C$ and $A D$ is the bisector of $\angle A$.
Prove that :
(i) $\triangle ADB \equiv \triangle ADC$
(ii) $\angle B =\angle C$
(iii) $BD = DC$
(iv) $AD \perp BC$

Answer

self

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Question 134 Marks

In the adjoining figure, $\triangle A B C$ is an isosceles triangle in which $A B=A C$ and $A D$ is a median.
Prove that :
(i) $\triangle ADB \cong \triangle ADC$
(ii) $\angle BAD =\angle CAD$

Answer

self

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Question 144 Marks

In the given figure, we have $AC \perp CD , BC \perp CD$ and $DA = DB$. Prove that: $CA = CB$.

Answer

[Hint : Prove that $\triangle DCA \cong \triangle DCB$ ]

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MATHS [4 marks sum]

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