in RD Sharma pg 10 52 question 6 (iv) is false please explain fast pls - Maths - Congruent Triangles

Question

in RD Sharma pg 10 52 question 6 (iv) is false please explain
fast pls

Manbar Singh · Accepted Answer

The given statement is , If the altitude from one vertex of a ∆ bisects opposite side, then∆ may be isosceles
The above statement is false, as we know that, If the altitude from one vertex of a ∆ bisects opposite side, then ∆ is always isosceles
Here is the proof
Consider a ∆ ABC, in which AD⊥BC and also AD bisects BC

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/1(237)%20png"
style="width: 279px; height: 225px;">
In ∆ADB and ∆ADC     AD = AD           common∠ADB = ∠ADC    90° each     BD = DC          as AD bisects BC⇒∆ADB ≅∆ADC  SAS⇒AB = AC   CPCT⇒∆ABC is an isosceles ∆

Hope this would have cleared your doubt

in RD Sharma pg 10.52 question 6 (iv) is false. please explain. fast pls.