1.In Δ PQR, D is the mid-point of
PD is ____.
Is QM = MR?
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.
(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.
(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.
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:
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.
👍👍👍