Mathematics – Class 7 – Chapter 6 – The Triangle And Its Properties – Exercise 6.1 – NCERT Exercise Solution

1.In Δ PQR, D is the mid-point of

PD is ____.

Is QM = MR?

Mathematics - Class 7 - Chapter 6 - The Triangle And Its Properties - Exercise 6.1 - NCERT Exercise Solution

Solution:

PM is Altitude.

PD is Median.

No, QM ≠ MR because, it is given that D is the mid-point of QR.

2. Draw rough sketches for the following:

(a) In ΔABC, BE is a median.

Solution:

We know that the median connects a vertex of a triangle to the mid-point of the opposite side.

Mathematics - Class 7 - Chapter 6 - The Triangle And Its Properties - Exercise 6.1 - NCERT Exercise Solution

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

Solution:

We know that altitude has one end point at a vertex of the triangle and the other on the line containing the opposite side.

Mathematics - Class 7 - Chapter 6 - The Triangle And Its Properties - Exercise 6.1 - NCERT Exercise Solution

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

Solution:

In this figure we observe for ΔXYZ, i.e YL is an altitude drawn exteriorly to side XZ which is extended up to point L.

Mathematics - Class 7 - Chapter 6 - The Triangle And Its Properties - Exercise 6.1 - NCERT Exercise Solution

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

Solution:

First, we draw an isosceles triangle PQR:

Mathematics - Class 7 - Chapter 6 - The Triangle And Its Properties - Exercise 6.1 - NCERT Exercise Solution

We draw a Line segment PS ⊥ BC, which is an altitude for triangle PQR.

Now, we observe that the length of QS and SR is also the same.

So, PS is also a median of triangle PQR.

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