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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, 01:12: PM
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

ADC is common to both triangle .

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 .

DSR = DAC ( corrseponding angles are equal )
DRS = DCA ( corrseponding angles are equal )
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, 07:54: PM

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