Criteria for Congruence of Triangles

In Fig. X and Y are two points on equal sides $AB$ and $AC$ of a $∆ABC$ such that $AX = AY$. Prove that $XC = YB$.
  

$AD$ and $BC$ are equal perpendiculars to a line segment $AB$. Then $CD$ _____ $AB$. [bisects/trisects]

If $AD$ is an altitude of an isosceles triangle $ABC$ in which $AB = AC$. Then:

$ABC$ is an isosceles triangle in which altitudes $BE$ and $CF$ are drawn to equal sides $AC$ and $AB$ respectively. Then:

If $E$ and $F$ are the midpoints of equal sides $AB$ and $AC$ of a triangle $ABC$. Then:

What are the Rules of Congruency?

Line $l$ is the bisector of an angle $\mathrm{\angle }A$ and $B$ is any point on $l$. $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $\mathrm{\angle }A$. Is $△APB\cong △AQB$ (Yes/No) ?

In quadrilateral $ACBD, AC=AD$ and $AB$ bisects $\angle A$ (see given figure). If $△ABC\cong △ABD.$ Is $BC=$$BD$ (Yes/No) ?

$ABC$ is an isosceles triangle with $AB=AC$. $BD$ and $CE$ are two medians of the triangle. Then $BD=$........

$\mathrm{A}\mathrm{B}\mathrm{C}$ is an isosceles triangle in which altitudes $\mathrm{B}\mathrm{E}$ and $\mathrm{C}\mathrm{F}$ are drawn to equal sides $\mathrm{A}\mathrm{C}$ and $\mathrm{A}\mathrm{B}$ respectively as shown in figure. The altitudes of the triangle are _____. (equal/unequal)

Which of the following is not a criterion for congruence of triangles?

Find the measure of variable in the given pair of congruent figures. All lengths are in centimetres. (Write the answer without unit)

How will you find a point $P$ inside $BC$ of $△ABC$ which is equidistant from $AB$ and $AC$.

If two equal chords of a circle intersect each other, then prove their successive parts will be equal to their corresponding parts . 

In the figure $△\mathrm{TOP}\equiv △\mathrm{ARM}$. Explain why?

In the figure, $\mathrm{PQ}\equiv \mathrm{TS},\mathrm{Q}$ is midpoint of $\mathrm{PR}$, $\mathrm{S}$ is the midpoint $\mathrm{TR}$ and $\angle \mathrm{PQU}\equiv \angle \mathrm{TSU}$. Prove that $\mathrm{QU}\equiv \mathrm{SU}$

If $△\mathrm{WAR}\cong △\mathrm{MOB}$, name the additional pair of corresponding parts. Name the criterion used here.

In the given figure, if $\mathrm{SW}\cong \mathrm{SE}$ and $\angle \mathrm{NWO}\cong \angle \mathrm{NEO}$. Then, prove that $\mathrm{NS}$ bisects $\mathrm{WE}$ and $\angle \mathrm{NOW}=90°$.

In triangles $ABC$ and $DEF$, $AB=FD$  and $\angle A=\angle D$ . The two triangles will be congruent by $\mathrm{SAS}$ axiom if :

The correct criterion for $△\mathrm{BGE}\cong △\mathrm{BGF}$ is