**The Triangle and Its Properties**

**Exercise 6.1**

1). In D PQR, D is the mid-point of QR.

PM is _________________.

PD is _________________.

Is QM = MR?

Answer:

PM is altitude.

PD is median.

Is QM = MR?

No QM ≠ MR

2). Draw rough sketches for the following:

(a) In DABC, BE is a median.

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

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

Solution

(a) In DABC, BE is a median.

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

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

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

DABC is an isosceles triangle with AB = AC

Draw AD median of the DABC

Now measure ÐADC with the help of a protractor

We find that ÐADC = 900

Thus, AD is meadian and also altitude of DABC.

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