Class 12 Exam > Class 12 Videos > Showing angles have same measure - Angles and intersecting lines, Geometry, Mathematics
Showing angles have same measure - Angles and intersecting lines, Geometry, Mathematics Video Lecture - Class 12
FAQs on Showing angles have same measure - Angles and intersecting lines, Geometry, Mathematics Video Lecture - Class 12
| 1. How do you prove that angles formed by intersecting lines are congruent? |  |
| 2. Can angles formed by two parallel lines intersected by a transversal have the same measure? | |
Ans. Yes, angles formed by two parallel lines intersected by a transversal can have the same measure. When a transversal intersects two parallel lines, corresponding angles, alternate interior angles, and alternate exterior angles are all congruent. Therefore, if two angles are corresponding, alternate interior, or alternate exterior angles, they will have the same measure.
| 3. Are all angles formed by intersecting lines congruent? | |
Ans. No, not all angles formed by intersecting lines are congruent. When two lines intersect, they form four angles at the intersection point. While opposite angles are congruent, the other two angles, known as adjacent angles, may have different measures. Adjacent angles are supplementary, which means their measures add up to 180 degrees, but they can have different individual measures.
| 4. How can we determine if two angles formed by intersecting lines are congruent using a protractor? | |
Ans. To determine if two angles formed by intersecting lines are congruent using a protractor, you need to measure the angles. Place the protractor on one of the angles, aligning the center of the protractor with the vertex of the angle. Then, read the measure of the angle from the protractor's scale. Repeat the same process for the other angle. If the measures of both angles are equal, then they are congruent.
| 5. Can angles formed by intersecting lines have different measures if the lines are perpendicular? | |
Ans. No, if two lines are perpendicular to each other, the angles formed by their intersection will always have the same measure. Perpendicular lines form four right angles at their intersection point, and by definition, right angles have a measure of 90 degrees. Therefore, all angles formed by the intersection of perpendicular lines will be congruent and measure 90 degrees.
Text Transcript from Video
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.
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.
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About this Video
Apr 11, 2025
Last updated
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