angle ABD and angle ACE are exterior angles o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(N/A) Let $\angle ABC = \beta$ and $\angle ACB = \gamma$. Since $\angle ABD$ is an exterior angle at vertex $B$,$\angle ABD = 180^\circ - \beta$. Sinc

Vedclass · Accepted Answer

$N$/$A$

Vedclass · Answer

(N/A) Let $\angle ABC = \beta$ and $\angle ACB = \gamma$. Since $\angle ABD$ is an exterior angle at vertex $B$,$\angle ABD = 180^\circ - \beta$. Since $\angle ACE$ is an exterior angle at vertex $C$,$\angle ACE = 180^\circ - \gamma$. Given that $\angle ABD > \angle ACE$,we substitute the expressions: $180^\circ - \beta > 180^\circ - \gamma$. Subtracting $180^\circ$ from both sides,we get $-\beta > -\gamma$. Multiplying by $-1$ reverses the inequality sign: $\beta Since $\angle ACB (\gamma) > \angle ABC (\beta)$,the side opposite to the larger angle is longer. Therefore,the side opposite to $\angle ACB$ is $AB$ and the side opposite to $\angle ABC$ is $AC$. Thus,$AB > AC$ is incorrect based on the standard exterior angle theorem logic; if $\angle ABD > \angle ACE$,then $\angle ACB > \angle ABC$,which implies $AB > AC$ is false,rather $AC > AB$ is true.

$\angle ABD$ and $\angle ACE$ are exterior angles of $\Delta ABC$. If $\angle ABD > \angle ACE$,then prove that $AC > AB$.

Similar Questions

If $\Delta PRQ \cong \Delta ZXY,$ then in $\Delta XYZ,$ which angle is equal to $\angle R$?

$ABC$ and $DBC$ are two triangles on the same base $BC$ such that $A$ and $D$ lie on the opposite sides of $BC$,$AB = AC$ and $DB = DC$. Show that $AD$ is the perpendicular bisector of $BC$.

In $\Delta PQR$,$X$ is the midpoint of $QR$. $XY$ and $XZ$ are altitudes from $X$ on $PQ$ and $PR$ respectively. If $XY = XZ$,then prove that $\Delta PQR$ is an isosceles triangle.

In $\triangle ABC$,$AB = AC$ and $\angle B = 50^{\circ}$. Then $\angle C$ is equal to (in $^{\circ}$)

Two sides of a triangle are of lengths $5\, cm$ and $1.5\, cm$. The length of the third side of the triangle cannot be (in $cm$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module