Question

2. Prove that ABCs boxeles if(0) Altinde AD Misects (0) Median AD is perpendicular to the base BC.​

Answer 1

Step-by-step explanation:

Here is a solution without any trigonometry or calculations.

Let AH be the altitude of triangle ΔABC through vertex A , i.e. the segment AH is perpendicular to AC with H on AC . The angle ∠BCH=∠BCA=30∘ in the right-angled triangle BCH yields that ∠CBH=60∘ . Furthermore, D is the midpoint of segment BC , so HD is the median of the right angled triangle ΔBCH which allows us to conclude that triangle BDH is equilateral and that BD=CD=HD=HB . Moreover, ∠CHD=30 .