Class 7 The Triangle and its Properties Ex 6.1

1. In Δ PQR, D is the mid-point of  .

(i) is ___.

Solution:-

Altitude

An altitude has one endpoint at a vertex of the triangle and another 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 another 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 the same.

Solution:-

Draw a line segment PS ⊥ QR. 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.