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Asked by dipanshupanwar144 | 03 Dec, 2023, 19:23: PM
Qn.12

QRS is common to ΔRQS and ΔRPT .
RQS = RPT ( Given )
Since RQS and RPT are corrsponding angles and they are equal , hence QS || PT
Hence PTR = QSR  ( because they are corresponding angles )

Since three  angles of ΔRQS are equal to respective angles of ΔRPT ,  ΔRQS and ΔRPT are similar by AAA similarity criterion.

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Qn. 13

3π is irrational number because π is irrational

5√5 is irrational because √5 is irrational

0.345710651372849.... is irrational because this nonterminating decimal number

0.3466666.... is rational number because this recurring decimal number

0.3466666...   = 0.34 + 0.0066666.....

0.3466666...   = (34/100) + (6/100) (0.11111.....)

0.3466666...   = (34/100) + (6/100)(1/9) = 312/900 = 78/225

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Qn.14

if we consider ΔPQR and ΔZYX, QPR = YZX = 60o
Respective sides of these angles are in same ratio as given below

XZ/PR  = YZ/QR = 1.5

Hence ΔPQR and ΔZYX are similar by SAS criterion

ΔLMN does not show any similarity with other triangles .
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