Let's move on, let's learn something interesting about area of triangles, let's say we have two parallel
lines over here and I marked this SBC.
Now, let me construct a triangle by choosing one point on this line.
Let that be.
And I joined with B and C and I get triangle ABC.
Now, let me choose another point on this line.
That's the and I join David BNC and I get Triangle DBC.
Now, let me take one more point on this line.
Let that be E and I joined with B and C and I get triangle EBC.
Now the between this line and B C that is A, right.
That's the perpendicular distance between two parallel lines.
That is it.
Now you will see that the area of Triangle ABC is equal to the area of Triangle BBC and that is equal
to the triangle of E, B, C, because area is half into base, into height.
And the height is the same thing for these three triangles because they are triangles between parallel
lines and these three triangles have the same base B.C. So poor area of Wrangell.
ABC is equal to area of triangle, BBC is equal to area of triangle EBC and that is equal to half each
in two B.C. because the base, they have a common base and the height is the same for these three triangles.
Now you will see.
So what does that mean?
Area of triangles.
With the same base.
And between parallel lines.
Is the same.
Right now, you can note that these three triangles are not congruent, right, you can see that if
you superimpose ABC on top of BBC, they will not exactly match, right?
So they are not congruent.
So it's not necessary that if you have two triangles of the same area, that they be congruent.
But the reverse is true.
If two triangles are congruent, then they definitely have the same area to quickly summarize triangles
with the same base and between parallel lines have the same area because we have seen the formula for
area of triangles, half in the base into height.