Exercise 12.1
Question 1
$\begin{array}{ll}A B=F E & \angle A=\angle F \\ B C=E D & \angle B=\angle E \\ A C=F D & \angle C=\angle D\end{array}$
Question 2
(i)$\angle C$
(ii)$\overline{C A}$
(iii)$\angle A$
(iv)$\overline{B A}$
Question 3
(i) $\overline{B C}=\overline{P R}$
$\overline{A B}=$ $\overline{Qp}$
$\overline{A C}=\overline{Q R}$
∴ By using SSS Congruence Rule
$\triangle A B C \cong \triangle Q P R$
(ii) $\overline{Q R} \neq \overline{A B}$
$\overline{PR}=\overline{A C}$
$\overline{PQ}=B C$
As one side is not equal both are not congruent
Question 4
(i) In $\triangle A B D, \triangle A C D$
$\overline{A B}=\overline{A C}$
$\overline{A D}=\overline{A D}$
$\overline{B D}=\overline{C D}$
(ii) By sss triangle congruency
$\triangle A B D \cong \triangle A D C$
(i) $\overlin
(iii) $\angle B=\angle C$ (∵Corresponding congruent parts)
Question 5
{A B}=\overline{A C}$
$\overline{A D}=\overline{A D}$
$\overline{B D}=\overline{C D}$ (∵D is mid point of BC)
(ii) By SSS triangle congruency
$\triangle A D B \cong \triangle A D C$
(iii) $\angle B=\angle C$ (∵Corresponding congruent parts)
Question 6
(i) $\overline{A B}=\overline{D E}$
$\overline{A C}=\overline{D F}$
$\angle A \neq \angle D$
∴ Triangle are not congruent
(ii) $\overline{A C}=\overline{R P}$
$\overline{B C}=\overline{Q O}$
$\angle C=\angle P$
By SAS congruency
$\triangle A B C \cong \triangle R Q P$
(iii) $\overline{D F}=\overline{P Q}$
$\overline{E F}=\overline{R Q}$
$\angle F=\angle Q$
By SAS Congruency
$\triangle D E F \cong \triangle P R Q$
(iv)$\overline{A B}=\overline{P Q}$
$\overline{B C}=\overline{Q R}$
$\angle B=\angle R=80^{\circ}$(but they are not congruent part)
So given , triangle are not congruent
Question 7
$\angle P=\angle F$
Question 8
(a) (i) $A R=P E$
(ii) $\rangle R T=E N$
(iii)AT =P N
(b) (i) $R T=E N$
(ii) $P N=A T$
Question 9
(i) Given
(ii) Given
(iii) Common side
(iv) SAS rule of congruency
Question 10
(i) $\overline{R S}=\overline{P Q}$
$\angle R=\angle P$
$\overline{D R}=\overline{R P}$
(ii) By SAS congruency
$\triangle P S R \cong \triangle R O P$
(iii) Yes, congruent parts
(iv) Yes, congruent parts
Question 11
(i) $\overline{A B}=\overline{D C}$
$\angle B=\angle C$
$\overline{B C}=\overline{C B}$
(ii) Yes, By SAS congruency of triangle
(iii) Yes, congruent parts are equal
Question 12
(i) $\overline{A C}=\overline{A D}$
$\angle A=\angle A$
$\overline{A B}=\overline{A B}$
(ii) Yes, $\triangle A B C \cong \triangle A B D$ , by SAS congruency
(iii) Yes, congruent parts
(iv) yes , congruent parts
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