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In δAbc, X is the Mid-point of Ab, and Y is the Mid-point of Ac. by and Cx Are Produced and Meet the Straight Line Through a Parallel to Bc at P and Q Respectively. Prove Ap = Aq. - Mathematics

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Question

In ΔABC, X is the mid-point of AB, and Y is the mid-point of AC. BY and CX are produced and meet the straight line through A parallel to BC at P and Q respectively. Prove AP = AQ.

Sum
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Solution


Join X and Y
In ΔABP,
X and Y are the mid-points of AB and AC respectively
Therefore, XY || BC
Since BC || AP
⇒ XY || AP and XY || AQ

∴ XY = `(1)/(2)"AP"` .......(i)

XY = `(1)/(2)"AQ"` ...........(ii)

From (i) and (ii)
⇒ `(1)/(2)"AP" = (1)/(2)"AQ"`

⇒ AP = AQ.

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Chapter 15: Mid-point and Intercept Theorems - Exercise 15.1

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Frank Mathematics [English] Class 9 ICSE
Chapter 15 Mid-point and Intercept Theorems
Exercise 15.1 | Q 23
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