Properties of a Triangle

In $∆ABC$, $AB=AC$ and $BC$ is produced to $D$. From $D$, $DE$ is drawn perpendicular to $BA$ produced and $DF$ is drawn perpendicular to $AC$ produced. Prove that $BD$ bisects $\angle EDF$

The circumcentre of triangle $ABC$is $O$. If angle $OBA=35°$ and $\angle OCA=25°$, then the value of angle $OBC$ is

In $∆ABC$, $AB=AC$ and $BC$ is produced to $D$. From $D$, $DE$ is drawn perpendicular to $BA$ produced and $DF$ is drawn perpendicular to $AC$ produced. Prove that $BD$ bisects $\angle EDF$

Does the median bisect the angles?

The figure below consists of a square and an equilateral triangle connected together with a common side.

What is the measure of $x$?

In the diagram below, points $Q \text{and} S$ lie on a circle with centre $O$. $SR$ is a tangent to the circle at $S$. $\angle QRS= 40° \text{and} \angle SOQ= 80°$. Prove that $∆QSR$ is isosceles.

$ABC$ is an isosceles triangle with $\angle A={40}^{\circ }$ and $AB=AC.$

$ABDE$ is a square drawn on the side $AB$ of $∆ABC.$

Find the measure of angles marked as $a,b,c,d.$

In the figure, $AB=BC, AC=CD$ and $\angle D=30°$ find $\angle BCA \text{and} \angle ABC$.

If one side of an isosceles triangle inscribed in a circle passes through the centre of a circle with radius $\frac{P}{4}$ then perimeter of a triangle is ________

$MNP$ is an isosceles triangle with $MN=NP$, point $R$ is on $NP$ such that $PR=4 \mathrm{cm}$. The perimeter of triangle is $24 \mathrm{cm}$ with $MP=6 \mathrm{cm}$. Then length of $NR$ is _____.

Prove that all the angles of equilateral triangle are equal.

Prove that the sides opposite to equal angles of a triangle are equal.

Prove that in a triangle, angles opposite to equal sides are equal.

A triangle is called an equilateral triangle when all its sides are equal in length.

Find the measure of each exterior angle of an equilateral triangle.

In $△ABC, AB=AC$ and $\angle A = 50°.$ Find the measure of $\angle B.$

The equation of the base of an equilateral triangle is $x+y-2=0$. If one of its vertex is $\left(2,-1\right)$, then area of the triangle is

If the centroid of the triangle formed by points $\left(a,b\right),\left(b,c\right),\left(c,a\right)$ is at the origin, then $a^3+b^3+c^3$ is equal to 

A triangle $ABC$ has $a, b,$ and $c$ such that $2a^2=3b^2+c$ and $b=6.$ Calculate the length of the median to side $c.$

In the figure, $AH=2\sqrt{5}$ and $m^2+n^2=41$. Find $b·c$