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Chapter 6 The Triangles and its Properties Ex 6.1 Solutions

Question - 1 : - In Δ PQR, D is the mid-point of .

(i)  is ___.

(ii) PD is ___.

(iii) Is QM = MR?

Answer - 1 : -

(i) 
Altitude
An altitude has one end point at a vertex of the triangle and other on the line containing the opposite side.
(ii)
Median
A median connects a vertex of a triangle to the mid-point of the opposite side.
(iii) 
No, QM ≠ MR because, D is the mid-point of QR.

Question - 2 : -
Draw rough sketches for the following:
(a) In ΔABC, BE is a median.
(b) In ΔPQR, PQ and PR are altitudes of the triangle.
(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.

Answer - 2 : -

(a) 
A median connects a vertex of a triangle to the mid-point of the opposite side.
 
(b) 
 
An altitude has one end point at a vertex of the triangle and other on the line containing the opposite side.
(c) 
 
In the figure we may observe that for ΔXYZ, YL is an altitude drawn exteriorly to side XZ which is extended up to point L.

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