Triangle PQR is formed by connecting the midpoints of the side of triangle MNO. The lengths of the sides of triangle PQR are sho

Question

9 months ago

7

wn. What is the length of MN? Figures not necessarily drawn to scale.

1 answer:

stiv31 [10] · Answer 1 · 2024-09-19T10:21:03+03:00

The length of segment $\overline{MN}$ found using properties of an equilateral triangle and segment addition postulate is 10

<h3>What is segment addition postulate?</h3>

Segment addition postulate states that a line AC contains a point B if we have AB + BC = AC

The sides of ∆PQR are equal to 5, therefore, ∆PQR is an equilateral triangle

According to the mid segment theorem, we have;

RQ || MN

RQ = 0.5 × MN

RP || ON

RP = 0.5 × ON

PQ || MO

PQ = 0.5 × MO

Therefore, from alternate interior angles theorem, we have;

‹PRQ = ‹RPM

‹PQR = ‹QPN

‹QRP = ‹RQO

However, ‹PRQ = ‹PQR = ‹QPR = 60°, which gives;

∆MRP and ∆QPN are equilateral triangles of side length 5

From which we have;

MR = RP = MP = 5

PN = QN = PQ = 5

MN = MP + PN; Segment addition postulate

Therefore;

MN = 5 + 5 = 10

Learn more about segment addition postulate here:

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