CBSE Class 10 Answered
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![question image](http://images.topperlearning.com/topper/new-ate/top_mob170161161712561750263deed97e-2469-4d46-a9e7-360f5cc985d3.jpg)
Asked by dipanshupanwar144 | 03 Dec, 2023, 19:23: PM
Qn.12
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/e1f9d7aa70fa857b4986436982b2ab83656ca055706cf7.11204000f1.png)
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
Since
RQS and
RPT are corrsponding angles and they are equal , hence QS || PT
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
Hence
PTR =
QSR ( because they are corresponding angles )
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
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
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
![angle](https://images.topperlearning.com/topper/tinymce/cache/b26763ff7db2ff496dbc2682f516d58a.png)
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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