NCERT Solutions Class 7th Math Chapter – 6 The Triangle and its Properties Exercise – 6.1

1. In Δ PQR, D is the mid-point of

Solution: Altitude
An altitude has one endpoint at a vertex of the triangle and other on the line containing the opposite side.

(ii) PD is ____.
Solution: Median
A median connects a vertex of a triangle to the mid-point of the opposite side.

(iii) Is QM = MR?
Solution: No, QM ≠ MR because D is the mid-point of QR.

2. Draw rough sketches for the following:

(a) In ΔABC, BE is a median.

Solution: A median connects a vertex of a triangle to the mid-point of the opposite side.

(b) In ΔPQR, PQ and PR are altitudes of the triangle.

Solution:

An altitude has one endpoint at a vertex of the triangle and other on the line containing the opposite side.

(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.

Solution:

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.

3. Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Solution:

Draw a Line segment PS ⊥ BC. It is an altitude for this triangle. Here we observe that the length of QS and SR is also the same. So PS is also a median of this triangle.