Video Transcript
Fill in the blanks. The first step to construct a
congruent angle to a given angle after drawing a ray is to draw what from the vertex
of the first angle, then to draw what from the vertex of the second angle.
Let’s go through the process of
constructing a congruent angle step by step so we can answer this question. We start with a given angle; let’s
call it angle 𝐴𝐵𝐶. We begin the construction of our
angle, which is congruent to angle 𝐴𝐵𝐶, by drawing a ray for the base leg of our
new angle. Let’s call the vertex of our newly
constructed angle 𝐸. And to make it easier to refer to
parts of our construction, let’s add a point 𝐷 to the right of 𝐸 along our
ray.
Now, we’ve reached the first
blank. We’ve drawn a ray for our new
construction. What do we do next? We need to place the point of our
compasses on 𝐵, the vertex of the first angle, and open up the radius a suitable
distance so that we can draw a large arc which cuts both 𝐵𝐴 and 𝐵𝐶. The larger it is, the more accurate
our construction is likely to be. But remember that it must be small
enough to intersect both 𝐵𝐴 and 𝐵𝐶. Now, we need to keep the same
radius, place the point of our compasses at 𝐸, the vertex of the second congruent
angle, and draw a similar arc.
Now, we have enough information to
fill in both blanks in the question. The first blank was an arc with
suitable radius, that is, large enough to be accurate but small enough that it will
intersect both legs of the angle. And the second blank was an arc
with the same radius.
Now, to complete our construction,
we put the point of our compasses at the point of intersection between our arc and
leg 𝐵𝐴 and open them so the point of the pencil touches the point of intersection
of the arc and leg 𝐵𝐶. Carefully keeping the radius
unchanged, we place the point of our compasses at the point of intersection between
our second arc and leg 𝐸𝐷. We then draw an arc that intersects
the second arc. Finally, we can draw another ray
from 𝐸 through this point of intersection. And we have an angle which is
congruent to our first angle.
