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the obligatory will fan will medal
okay there are some basic triangle theorems you have to know 3 main ones are AAS, SSS, and SAS theorems that if satisfied means the 2 triangles are congruent
the next is parallel lines and which angles are equal lets start there!
Lets first draw 2 parallel lines and see if we can find something about an intersection of a line through them
oky we know that angle 1 = angle 2 , as these are opposite angles and opposite angles have ot be equal
we can see this very easily as angles along a straight line add up to 180
yes they do
you see how that angle in between 1 and 2, is 180 - angle 2 or 180 - angle 1
this means angle 2 and 1 have to be the same
tell me if you understand that
im following so far
okay now you know why opposite angles are equal, lets move on
im not sure exactly how to prove that one, but take that as face value its more intuitive, it must be true kinda thing
like think about it it angle 3 is not the same as angle 1
then these lines cannot be parallel right
beccause somewhere at some point they will intersect and form a triangle
okay so thats all we need to solve your question
now lets make a parallelogram
these angles have to be the same here
from the parallel lines we saw before its like this Z pattern
can you really see that
yes i can
can you tell me what other angles have to be the same from this same idea
yep that is right, now what does that mean about the remaining angle
to be honest, im not sure.
okay lets think about it
all angles in a triangle add upto what
and since theres 2 in the parrelelogram its 360 degrees
okay now u see both triangles in there have an angle that is a and angle that is b
what is the remaining angle?
the remaining angles have to be equal too... tell me why
because of the alternate exterior?
forget that stuff, think logic
we know all the angles add upto 180 right
a+b+the remaining angle is 180
then the same remaining angle must be on the bottom too as there is an a and a b
so we have 3 samme angles and a side that is the same, as the diagonal is shared
so by AAS rule, these triangles are congruent
thank you, later on today i will reward you with owl bucks for your torubles.