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Constructing a Copy of a Given Angle Video Lecture - Class 6
FAQs on Constructing a Copy of a Given Angle Video Lecture - Class 6
| 1. What is an angle in geometry? |  |
Ans. An angle in geometry is a figure formed by two rays or lines that share a common endpoint, called the vertex. It is usually measured in degrees or radians and is used to measure the amount of rotation or separation between the two rays.
| 2. What is a copy of an angle? | |
Ans. A copy of an angle refers to constructing an angle that is equal to a given angle. This can be done by using a compass and a straightedge to replicate the angle's measurements, ensuring that the size and orientation of the new angle are identical to the original angle.
| 3. How can I construct a copy of a given angle? | |
Ans. To construct a copy of a given angle, follow these steps:
1. Place the compass point at the vertex of the given angle and draw an arc that intersects both rays of the angle.
2. Without changing the compass width, place the compass point at the intersection of the arc and one of the rays, and draw another arc inside the angle.
3. Without changing the compass width, place the compass point at the intersection of the arc and the other ray, and draw a third arc that intersects the second arc.
4. Use a straightedge to draw a line connecting the vertex of the given angle with the intersection point of the second and third arcs. This line will be the copy of the given angle.
| 4. What are the properties of a copy of an angle? | |
Ans. A copy of an angle will have the same properties as the given angle. This means that the copy will have the same measure in degrees or radians, and the same orientation as the original angle. Additionally, the copy will have congruent corresponding angles and will be able to form similar triangles or other geometric figures with the same properties as the original angle.
| 5. Why is constructing a copy of an angle useful in geometry? | |
Ans. Constructing a copy of an angle is useful in geometry because it allows us to create identical angles in different locations or orientations. This is often necessary when working with geometric proofs, constructions, or solving problems involving angles. By being able to replicate angles accurately, we can establish relationships, solve equations, and make connections between different parts of a geometric figure.
Text Transcript from Video
constructing an angle congruent to the
given angle in this video we're gonna
learn how to construct an angle
congruent to a given angle for this
construction you're going to need a
protractor a compass a pencil and a
ruler or scale so let's learn this
method by use of an example consider the
example shown here here we have three
points a b and c with an angle be
measuring 35 degrees you can measure
this angle with a protractor as shown
so what we're trying to do is construct
another angle congruent to this angle
ABC the angle is congruent to the other
one if the two angles are equal with
this given angle on the left side of the
paper let's draw a new horizontal line
using a scale and pencil next to this
given angle let's mark two points P and
Q on this new line
now the first thing we have to do is
draw an arc on the given angle we do
this by using a compass with a
convenient radius and using B as the
center to cut the Rays ba and BC on the
arms of the given angle ABC the arc cuts
the angle ABC at points D and E
respectively as shown
now that we've cut our given angle at
points D and E we have to bring the
compass over to the right side of the
paper use P as the center and without
changing the radius of the compass draw
another extended arc which also
intersects the Ray PQ we're going to
mark this point as say G
now bringing our compass to the left
side of the paper again we need to
adjust our radius so that it's the same
as the distance from D to E now using G
as the center we draw another arc that
intersects the previous arc at say H
now that we have the points G and H all
we have to do now is use a scale to join
the points P and H for the Ray pH
our construction is complete but to
check this we're going to use a
protractor putting the center of the
protractor at point-p we measure the
angle and find it to be equal to 35
degrees the same as the left side
so you should observe that angle QP H is
equal to 35 degrees
since angle ABC is equal to angle Q pH
we say that the two angles are congruent
in other words angle QP H is congruent
to angle ABC
so as you can see if you know the
measure of an angle you can easily
construct another angle it's congruent
to it using this procedure
so that's how you construct an angle
congruent to a given angle in our case
angle QP H was equal to the given angle
angle ABC
given angle in this video we're gonna
learn how to construct an angle
congruent to a given angle for this
construction you're going to need a
protractor a compass a pencil and a
ruler or scale so let's learn this
method by use of an example consider the
example shown here here we have three
points a b and c with an angle be
measuring 35 degrees you can measure
this angle with a protractor as shown
so what we're trying to do is construct
another angle congruent to this angle
ABC the angle is congruent to the other
one if the two angles are equal with
this given angle on the left side of the
paper let's draw a new horizontal line
using a scale and pencil next to this
given angle let's mark two points P and
Q on this new line
now the first thing we have to do is
draw an arc on the given angle we do
this by using a compass with a
convenient radius and using B as the
center to cut the Rays ba and BC on the
arms of the given angle ABC the arc cuts
the angle ABC at points D and E
respectively as shown
now that we've cut our given angle at
points D and E we have to bring the
compass over to the right side of the
paper use P as the center and without
changing the radius of the compass draw
another extended arc which also
intersects the Ray PQ we're going to
mark this point as say G
now bringing our compass to the left
side of the paper again we need to
adjust our radius so that it's the same
as the distance from D to E now using G
as the center we draw another arc that
intersects the previous arc at say H
now that we have the points G and H all
we have to do now is use a scale to join
the points P and H for the Ray pH
our construction is complete but to
check this we're going to use a
protractor putting the center of the
protractor at point-p we measure the
angle and find it to be equal to 35
degrees the same as the left side
so you should observe that angle QP H is
equal to 35 degrees
since angle ABC is equal to angle Q pH
we say that the two angles are congruent
in other words angle QP H is congruent
to angle ABC
so as you can see if you know the
measure of an angle you can easily
construct another angle it's congruent
to it using this procedure
so that's how you construct an angle
congruent to a given angle in our case
angle QP H was equal to the given angle
angle ABC
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Oct 22, 2025
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