### Video Transcript

In the following figure,
triangle π΄ prime π΅ prime πΆ prime is the image of triangle π΄π΅πΆ by
reflection in the line πΏ. (1) Fill in the blanks. The length of π΄ prime πΆ prime
equals blank centimeters, and the length of π΄ prime π΅ prime equals blank
centimeters. (2) Fill in the blanks. Line segment π΄π΄ prime is
blank to line segment π΅π΅ prime, and line segment πΆπΆ prime is blank to line
πΏ. (3) Find the measure of angle
π΄.

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 π΄πΆ is congruent
to line segment π΄ prime πΆ prime. They must have the same
lengths. Since line segment π΄πΆ is four
centimeters, line segment π΄ prime πΆ prime must also be four centimeters. And we put four in the first
blank space.

Next, line segment π΄π΅ must be
congruent to line segment π΄ prime π΅ prime. And so, π΄ prime π΅ prime must
be six centimeters in length. And six goes in our second
blank space.

Letβs now consider question
(2). First, we add line segments
π΄π΄ prime and π΅π΅ prime to the diagram. We know that these line
segments must be perpendicular to the mirror line. If theyβre 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
πΆπΆ prime is perpendicular to line πΏ.

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 π΄ must be equal to the measure of angle π΄ prime. Angle π΄ prime is 31 degrees,
so angle π΄ is also 31 degrees.

And so, we have filled in the
blanks. The correct entries were four,
six, parallel, perpendicular, and 31 degrees.