In Δ ABC, X is the midpoint of BC.
AP is _____________
AX is _____________
Is BP = PC?
BX = XC
Therefore, AP is altitude.
AX is a median.
No, BP ≠ PC as X is the midpoint of BC
Draw a sketch for the following:
(i) In Δ PQR, QX is a median
(ii) In Δ ABC, AB and AC are altitudes of a triangle.
(iii) In ABC, BP is an altitude in the exterior of a triangle.
(i) Here, QX is a median in ΔPQR and PX = XR
(ii) Here, AB and AC are the altitudes of the ΔABC and CA ^ BA
(iii) BP is an altitude in the exterior of ΔABC
Verify by drawing a diagram if the median and altitude of a isosceles triangle can be same.
Isosceles triangle means any two sides are same.
Take ΔPQR and draw the median when PQ= PR
PX is the median and altitude of the given triangle.