Find the measure of each side of the triangle AP Q if point B and point C are the mid points of the side AP and QArespectively-A- A P-6 cmPQ -8 cmQA -10 cmB- AP -6 cmPQ -10 cmQA -8 cmC- AP -8 cmPQ -10 cmQA -6 cmD- AP -6 cmPQ -12 cmQA -8 cm

The correct option is B AP = 6 cm PQ = 10 cm QA = 8 cmGiven, nbsp; AB = 3 cm, CA = 4cm and BC = 5 cm Since, point B and point C are the mid points. ∴AB = BP ...

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Standard IX

Mathematics

Mid-Point Theorem

Find the meas...

Question

Find the measure of each side of the triangle $△ A P Q$ if point B and point C are the mid points of the side AP and QA respectively.

AP = 6 cm
PQ = 8 cm
QA = 10 cm

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AP = 6 cm
PQ = 10 cm
QA = 8 cm

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AP = 8 cm
PQ = 10 cm
QA = 6 cm

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AP = 6 cm
PQ = 12 cm
QA = 8 cm

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Solution

The correct option is B AP = 6 cm
PQ = 10 cm
QA = 8 cm
Given,
AB = 3 cm, CA = 4cm and BC = 5 cm

Since, point B and point C are the mid points.
$∴$ AB = BP = 3 cm
$\Rightarrow$ AP = AB + BP = 3 + 3 = 6 cm
also, QC = CA = 4 cm
$\Rightarrow$ QA = QC + CA = 4 + 4 = 8 cm

We know that the line segments joining the mid points of the two sides of a triangle is parallel to the third side and also half of it.
$∴ B C = \frac{P Q}{2}$
$\Rightarrow P Q = B C \times 2 = 5 \times 2 = 10 c m$

Therefore, measure of the sides are
AP = 6 cm
PQ = 10 cm
QA = 8 cm

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Find the measure of each side of the triangle △APQ if point B and point C are the mid points of the side AP and QA respectively.

Find the measure of each side of the triangle $△ A P Q$ if point B and point C are the mid points of the side AP and QA respectively.