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State which pairs of triangles in Fig. 6.34 are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :

Q1   State which pairs of triangles in Fig. 6.34 are similar. Write the similarity criterion used by
        you for answering the question and also write the pairs of similar triangles in the symbolic
        form :

           

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(i) \angle A=\angle P=60 \degree

    \angle B=\angle Q=80 \degree

  \angle C=\angle R=40 \degree

 \therefore \triangle ABC \sim \triangle PQR     (By AAA)

So , \frac{AB}{QR}=\frac{BC}{RP}=\frac{CA}{PQ}

 

(ii) As corresponding sides of both triangle are proportional.

\therefore \triangle ABC \sim \triangle PQR    (By SSS)

 

(iii) Given triangles are not similar because corresponding sides are not proportional.

 

(iv) \triangle MNL \sim \triangle PQR  by SAS similarity criteria.

 

(v) Given triangles are not similar because corresponding angle is not contained by two corresponding sides

 

(vi) In \triangle DEF, we know that 

       \angle D+\angle E+\angle F=180 \degree

\Rightarrow 70 \degree+80 \degree+\angle F=180 \degree

\Rightarrow 150 \degree+\angle F=180 \degree

\Rightarrow \angle F=180 \degree-150 \degree=30 \degree

 

In \triangle PQR, we know that 

       \angle P+\angle Q+\angle R=180 \degree

\Rightarrow 30 \degree+80 \degree+\angle R=180 \degree

\Rightarrow 110 \degree+\angle R=180 \degree

\Rightarrow \angle R=180 \degree-110 \degree=70 \degree

 \angle Q=\angle P=70 \degree

    \angle E=\angle Q=80 \degree

  \angle F=\angle R=30 \degree

\therefore \triangle DEF\sim \triangle PQR   ( By AAA)

 

 

 

 

 

 

 

 

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