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## Angles

Current time:0:00Total duration:4:53

# Proving angles are congruent

## Video transcript

We have an interesting looking
diagram here. Let's see if we know a few things
about this diagram. Let's say we know that line MK is parallel to line NJ. So this line is parallel to this line. This is line MK, this is line NJ. Now, given that
and all the other information on this diagram, I'm hoping to prove that the measure
of this angle LMK is equal to the measure
of this angle over here and this angle is LNJ. Another way of writing this is; the measure of LMK is b
and the measure of LNK is a. So we want to prove that b is equal to a using all this information
that we know. Like always I encourage you
to try this on your own before I walk through it. Alright, let's walk through it. The first thing you might see is
I have a triangle formed up here, triangle MLK. What do we know about the measurement
of the interior angles of a triangle? The measures of the interior angles
of a triangle are going to add up to 180 degrees. We know that b,
which is the measure of this angle plus the measure of this angle, c plus the measure of this right angle,
which is plus 90 degrees is going to be equal to 180 degrees. And so if we subtract 90 degrees
from both sides we're going to get b plus c
is equal to 180 degrees minus 90 degrees. It's going to be 90 degrees. Or if we wanted to solve
explicitly for b we could subtract c from both sides, and we could write b is equal to
90 degrees minus c. So that's interesting,
that's one way of expressing b. Can we express a in a similar way? Once again, if at any point
you get inspired I encourage you to do that. If we look carefully we see that
we have triangle NLJ, this really big triangle,
it's really most of the diagram. What's interesting about NLJ
is that J is another right triangle, c is one of the measures
of one of the interior angles, and a is a measure of
the other interior angle. We can write something very similar, we can write a plus c
plus 90 degrees is going to be equal
to 180 degrees. So what can we do here? We can do the exact same process
to solve for a. If we subtract 90 from both sides
and we subtract c from both sides what do we get? We get a is equal to 90 degrees
and if you subtract c from both sides you're going to get 90 degrees minus c. Now this is interesting, b is equal to 90 degrees minus c
and a is equal to 90 degrees minus c. So 90 degrees minus c is equal to a,
it's also equal to b. Or, we can now say that
a must be equal to b, that the measure of angle LMK
which is b is equal to the measure of angle LNJ
which is equal to a.