In a triangle ABC with angle A

Question

(A) For two triangles to be similar,their corresponding angles must be equal. In $	riangle ABC$,the angles are ordered as $\angle A < \angle B < \ang

Vedclass · Accepted Answer

$	riangle ABD$

Vedclass · Answer

(A) For two triangles to be similar,their corresponding angles must be equal. In $	riangle ABC$,the angles are ordered as $\angle A Consider $	riangle ABD$. Since $D$ is on the interior of segment $BC$,$\angle ADB$ is an exterior angle to $	riangle ADC$,so $\angle ADB = \angle DAC + \angle C$. Thus,$\angle ADB > \angle C$. Since the largest angle of $	riangle ABC$ is $\angle C$,and $	riangle ABD$ contains an angle $\angle ADB$ which is strictly greater than $\angle C$,the set of angles in $	riangle ABD$ cannot be the same as the set of angles in $	riangle ABC$. Therefore,$	riangle ABD$ cannot be similar to $	riangle ABC$.Similarly,one can show that $	riangle BCE$ and $	riangle CAF$ cannot be similar to $	riangle ABC$ under general conditions. However,among the given options,$	riangle ABD$ is a standard example of a triangle formed by a cevian that cannot be similar to the original triangle due to the angle inequality constraints.

In a $\triangle ABC$ with $\angle A < \angle B < \angle C$,points $D, E, F$ are on the interior of segments $BC, CA, AB$ respectively. Which of the following triangles cannot be similar to $\triangle ABC$?

Similar Questions

The vertices of a triangle are $(at_1t_2, a(t_1 + t_2))$,$(at_2t_3, a(t_2 + t_3))$,and $(at_3t_1, a(t_3 + t_1))$. Find the coordinates of its orthocentre.

The area of the triangle bounded by the straight line $ax + by + c = 0$ $(a, b, c \neq 0)$ and the coordinate axes is

In an isosceles $\triangle ABC$,the coordinates of vertices $B$ and $C$ of the base $BC$ are $(3, 2)$ and $(2, 3)$ respectively. If the equation of the line $AB$ is $3y = 2x$,then the equation of the line $AC$ is

The equations of two altitudes of an equilateral triangle are $\sqrt{3}x - y + 8 - 4\sqrt{3} = 0$ and $\sqrt{3}x + y - 12 - 4\sqrt{3} = 0$. The equation of the third altitude is

The number of triangles formed by the lines $x-y+3=0$,$2x-y+3=0$,$3x-y+2=0$,and $x+y-3=0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module