Establishing Congruent Triangles

In $△ABC, \angle A=30°, \angle B=40°, \angle C=110°$. In $△PQR, \angle P=30°, \angle Q=40°, \angle R=110°$. A students says that $△ABC\cong △PQR$ by $AAA$ congruence criteria. Is he justified? Why or why not?

Triangle $ABC$ is an isosceles triangle and the line segment $AD$ is the angle bisector of the $\angle A$. Prove that $\Delta ADB$ is congruent to the $\Delta ADC$ by using SAS rule.

In the given isosceles triangle $△PQR$, prove that the altitude $PO$ bisects the base of the triangle $QR$.

State whether the following pair of triangles is congruent.

$△ABC: AB=10 \mathrm{cm}, \angle A=40°, \angle B=55°$

$△XYZ: XY=10 \mathrm{cm}, \angle Y=40°, \angle Z=85°$

Are these shapes congruent?

State the correspondence between the vertices.
$△CAB\cong △QRP$

If $△EFG\cong △LMN$, write the corresponding vertices.

Two equilateral triangles are congruent if:

Can two equilateral triangles always be congruent? Give reasons.

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

Isosceles triangle with equal sides as $5\mathrm{}\mathrm{c}\mathrm{m}$ and included angle as $55$.

    Right-angled triangle with measurements  $\stackrel{-}{\mathrm{L}\mathrm{M}}$ $=\mathrm{}4.7\mathrm{}\mathrm{c}\mathrm{m}$, $\stackrel{-}{\mathrm{L}\mathrm{N}}$ $=\mathrm{}5\mathrm{}\mathrm{c}\mathrm{m}$ and $\angle \mathrm{N}\mathrm{L}\mathrm{M}$ $=64°$.

Right-angled triangle with measurements $\stackrel{-}{\mathrm{A}\mathrm{C}\mathrm{}}=\mathrm{}7.5\mathrm{}\mathrm{c}\mathrm{m},$ $\stackrel{-}{\mathrm{A}\mathrm{B}\mathrm{}}=9\mathrm{}\mathrm{c}\mathrm{m}\mathrm{}$and $\mathrm{\angle }\mathrm{}=\mathrm{}60°$.

Right-angled triangle with measurements $\stackrel{-}{\mathrm{}\mathrm{A}\mathrm{B}}$ $=\mathrm{}8\mathrm{}\mathrm{c}\mathrm{m}\mathrm{}$and $\mathrm{B}\mathrm{C}\mathrm{}=\mathrm{}6\mathrm{}\mathrm{c}\mathrm{m}$ and the included angle is $90°$.

Construct a triangle $\mathrm{U}\mathrm{V}\mathrm{W}$ with $\mathrm{}\stackrel{-}{\mathrm{U}\mathrm{V}}\mathrm{}=\mathrm{}2.9\mathrm{}\mathrm{c}\mathrm{m}$, $\stackrel{-}{\mathrm{V}\mathrm{W}}=8.5\mathrm{c}\mathrm{m}$ and $\stackrel{-}{\mathrm{W}\mathrm{V}}$ $=6.2cm$. Classify this triangle on the basis of angles.

Is it possible to construct a triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ with $\stackrel{-}{\mathrm{B}\mathrm{C}}=9cm,\stackrel{-}{\mathrm{A}\mathrm{C}}=5\mathrm{c}\mathrm{m}$ and $\angle B={40}^o$? Justify your answer with a diagram.