give answer of Ques 12 and Ques 13...plzz step by step with figure. it's really urgent
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Question 12
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Question 13
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Given:P,Q,R are the mid points of sides BC,CA and AB of a triangle ABC. PR and BQ meet at X. CR and PQ meet at Y.
To Prove:
Proof: In Δ ABC, Q and R are the mid-points of sides AC and AB respectively.
⇒QR = BP [P is the mid-point of BC].
Using Mid-point Theorem, it can also be said that QR || BC.
⇒ QR || BP
In quadrilateral BPQR, BP || QR and BP = QR.
Thus, BPQR is a parallelogram
Now, the diagonals BQ and PR of the parallelogram BPQR bisect each other at X.
Thus, X is the mid-point of PR
Similarly, it can be formed that Y is the mid-point of PQ
In ΔPQR, X and Y are the mid-points of sides PR and PQ respectively
Hence Proved.
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Question 13
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Given:P,Q,R are the mid points of sides BC,CA and AB of a triangle ABC. PR and BQ meet at X. CR and PQ meet at Y.
To Prove:
Proof: In Δ ABC, Q and R are the mid-points of sides AC and AB respectively.
⇒QR = BP [P is the mid-point of BC].
Using Mid-point Theorem, it can also be said that QR || BC.
⇒ QR || BP
In quadrilateral BPQR, BP || QR and BP = QR.
Thus, BPQR is a parallelogram
Now, the diagonals BQ and PR of the parallelogram BPQR bisect each other at X.
Thus, X is the mid-point of PR
Similarly, it can be formed that Y is the mid-point of PQ
In ΔPQR, X and Y are the mid-points of sides PR and PQ respectively
Hence Proved.
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