Question

A scalene triangle is cut along one of the altitudes. How many lines of symmetry are there in the new triangles?

Answer 1

If triangles are either equilateral triangle or isosceles triangle, then line of symmetry will present .

Given $AB\ne BC\ne AC$

Now draw the altitude $AD$ from point $A$ to line $BC$

now check the length of each side of new triangles $\Delta ABD$ and $\Delta ACD$

In $\Delta ABD$

let us assume $BD=x$ and $AB=d$

using Pythagoras theorem in $\Delta ABD$

$A{B}^2=B{D}^2+A{D}^2$

$AD=\sqrt{d^2-x^2}$

if $d=\sqrt{2}x$, Then $AD=AD$ ,then there will be one line of symmetry present in $\Delta ABD$

Otherwise $AB\ne AD\ne BD$

similarly for $\Delta ACD$