CBSE Class 9 Answered
ABCD is quadrilateral in which P Q R S are mid points of the sides AB BC CD DA. AC is diagonal. show that SR is parallel to AC and SR= 1half 2 AC
Asked by aksharapatni | 30 Nov, 2023, 13:12: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/e9f143e9dfe58e53fd3337ca7abdbaeb6568952d36fe16.14895554g1.png)
Figure shows the quardilateral ABCD . P, Q, R and S are mid points of sides AB, BC, CD and DA respectively.
Let us consider Δ ADC and ΔSDR .
DS/DA = DR/DC = 1/2
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
SAS Similarity theorem states that if the two sides of a triangle are in the same proportion to the two sides of another triangle,
and the angle included by the two sides in both the triangles are same, then two triangles are similar.
Hence Δ ADC and ΔSDR are similar triangles .
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
Hence SR is parallel to AC.
By property of similar triangles
SR/AC = DS/ DA = DR/DC = 1/2
Answered by Thiyagarajan K | 30 Nov, 2023, 19:54: PM
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