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Question
In ΔPQR, PQ = 5 cm, QR = 12 cm, PR = 13 cm. M and N are mid-points of PQ and QR. The length of MN is ______.
Options
2.5 cm
6 cm
6.5 cm
none of these
MCQ
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Solution
In ΔPQR, PQ = 5 cm, QR = 12 cm, PR = 13 cm. M and N are mid-points of PQ and QR. The length of MN is 6.5 cm.
Explanation:
In triangle ΔPQR, we are given:
- PQ = 5 cm,
- QR = 12 cm,
- PR = 13 cm,
- M and N are midpoints of sides PQ and QR, respectively.
We are asked to find the length of segment MN.
Step 1: Apply the Midpoint Theorem:
The Midpoint Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the length of that third side.
In this case:
- M is the midpoint of PQ,
- N is the midpoint of QR.
So, segment MN is parallel to side PR and is half of its length.
Therefore, the length of MN is
`MN = 1/2 xx PR`
= `1/2 xx 13` cm
= 6.5 cm
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