Triangles - Congruency

Here are 3 questions i cant solve & when asking my teacher, he couldnt solve too

Question 1:

Triangle ABC and Triangle DEF are such

that AB=DE , AC=DF, AM Perpendicular to BC

and DN Perpendicular to EF . Prove that Triangle

ABC is Congurent to Triangle DEF

[In the figure

triangles are not joined. they are2 triangles

drawn, at side of each other & both triangles

doesnt haveany line connected.]

Question 2:

The Image of an object placed at point

A before a plane mirror LM is seen at the point

B by an observer at D. Prove that the image is

as far behined as the object is seen in front of

the mirror[No Figure Given]

Question 3:

in Triangle ABC, The bisectors of Angle B and

Angle C meet at P. Through P, a straight line MPN is

Drawn parallel to BC. Prove that MN = BM + CN

[No figure Given]

Note:Please show figures and stuff.