Question

Triangle PQR is formed by connecting the midpoints of the side of triangle MNO. The lengths of the sides of triangle PQR are shown. What is the length of MN? Figures not necessarily drawn to scale.

Answer 1

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

What is segment addition postulate?

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:

brainly.com/question/1721582

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