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In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =1. 1 : 32. 3 : 13. 2 : 14. 1 : 2 |
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Answer» Correct Answer - Option 4 : 1 : 2 Concept: If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Calculations: Given, In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Join AC and BP. ⇒ \(\angle\)AQP= CQB and \(\angle\)APQ= \(\angle\)CBQ If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent ⇒ \(\rm\triangle APQ ∼ \triangle CBQ\) ⇒ \(\rm \dfrac {AP}{BC}= \rm \dfrac{AQ}{QC}\) ⇒ AD = BC ⇒ \(\rm \dfrac {AP}{BC}= \rm \dfrac{AP}{AD} = \dfrac 1 2\) ⇒ \(\rm\rm \dfrac{AQ}{QC} = \dfrac 12\) Hence, In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC = 1 : 2 |
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