Video Transcript
In the following figure,
triangle 𝐴 prime 𝐵 prime 𝐶 prime is the image of triangle 𝐴𝐵𝐶 by
reflection in the line 𝐿. (1) Fill in the blanks. The length of 𝐴 prime 𝐶 prime
equals blank centimeters, and the length of 𝐴 prime 𝐵 prime equals blank
centimeters. (2) Fill in the blanks. Line segment 𝐴𝐴 prime is
blank to line segment 𝐵𝐵 prime, and line segment 𝐶𝐶 prime is blank to line
𝐿. (3) Find the measure of angle
𝐴.
Remember, when we reflect a
polygon in a mirror line, we create a second congruent polygon. This means that the two
triangles in our diagram are congruent. That in turn means that their
line segments and angle measures are equal. This fact helps us to answer
part (1). Line segment 𝐴𝐶 is congruent
to line segment 𝐴 prime 𝐶 prime. They must have the same
lengths. Since line segment 𝐴𝐶 is four
centimeters, line segment 𝐴 prime 𝐶 prime must also be four centimeters. And we put four in the first
blank space.
Next, line segment 𝐴𝐵 must be
congruent to line segment 𝐴 prime 𝐵 prime. And so, 𝐴 prime 𝐵 prime must
be six centimeters in length. And six goes in our second
blank space.
Let’s now consider question
(2). First, we add line segments
𝐴𝐴 prime and 𝐵𝐵 prime to the diagram. We know that these line
segments must be perpendicular to the mirror line. If they’re both perpendicular
to the mirror line, we can conclude some further information. That is, their alternate angles
are equal, and they must in fact be parallel to one another. To find the second blank word
in question (2), we add the line segment to the diagram. And of course, we know that
𝐶𝐶 prime is perpendicular to line 𝐿.
Finally, we consider question
(3). Remember, these two triangles
are congruent, which means they share angle measures. In particular, this means that
the measure of angle 𝐴 must be equal to the measure of angle 𝐴 prime. Angle 𝐴 prime is 31 degrees,
so angle 𝐴 is also 31 degrees.
And so, we have filled in the
blanks. The correct entries were four,
six, parallel, perpendicular, and 31 degrees.
