Page 188 - ICSE Math 6

Median of a triangle A

A median of a triangle is a line segment that joins the vertex of the
triangle to the midpoint of the opposite side.
In ∆ ABC drawn alongside, AD, BE and CF are the medians. The point F G E
G is the point of intersection of the medians and is known as centroid.

B D C
Altitude of a triangle
The perpendicular drawn from the vertex to the opposite side of a triangle A
is called its altitude. It is the shortest distance from the vertex to the
opposite side. M

In ∆ ABC drawn alongside, AL is the altitude drawn from the vertex A N O
to side BC. The other two altitudes are BM and CN. The point O is the

point of intersection of altitudes and is known as the orthocentre.
B L C
Example 6: In ∆ PQR given alongside, D is the midpoint of QR.
Answer the following. P

(a) PM is the ___________.
(b) PD is the ____________.
(c) Is QM = MR?

(d) Which among PQ, PM, PD and PR is the shortest? Q M D R
Solution: (a) PM is the altitude. (b) PD is the median.
(c) No, QM ≠ MR. (d) PM, as it is the perpendicular distance.

Example 7: Draw rough sketches for the following.
(a) In ∆ ABC, BE is a median.

(b) In ∆ PQR, PQ and PR are altitudes.
(c) In ∆ XYZ, YL is an altitude in the exterior.
(d) In ∆ FAN, FP is a median and AL is an altitude.

A R

Solution: (a) E (b)

B C P Q
F

Y

(c) (d)
L

Z X L
A P N

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