Video Transcript
In the figure, triangle ๐ด๐ต๐ถ and
triangle ๐ธ๐น๐ท are congruent. Work out the length of ๐ต๐ถ. Work out the length of ๐ธ๐น. Work out the measure of angle
๐ท๐ธ๐น.
In this question, weโve got two
triangles, triangle ๐ด๐ต๐ถ and triangle ๐ธ๐น๐ท. Weโre told that these two triangles
are congruent, which means that theyโre the same shape and size. Even if theyโre in a different
orientation, corresponding angles will be equal and corresponding pairs of sides
will be equal. In the first part of this question,
weโre asked to work out the length of ๐ต๐ถ. So letโs see if we can find the
corresponding side in the other triangle ๐ธ๐น๐ท to work out the length.
In some diagrams, itโs relatively
easy to find the corresponding side in a congruent triangle. But if not, we can always use the
congruency relationship. We are given that triangle ๐ด๐ต๐ถ
is congruent to triangle ๐ธ๐น๐ท. So that means if weโre looking at
the line ๐ต๐ถ in triangle ๐ด๐ต๐ถ, then it would be congruent with the line ๐น๐ท on
triangle ๐ธ๐น๐ท. Thatโs because in a congruency
relationship, the order of the letters is very important. On our diagram, weโre given that
the length of ๐น๐ท is 4.5. Therefore, the length of ๐ต๐ถ must
also be 4.5. And so our answer for the first
part of the question is that ๐ต๐ถ is 4.5 units long.
Letโs look at the second
question. Here, weโre asked to find the
length of ๐ธ๐น on triangle ๐ธ๐ท๐น. Using the congruency relationship,
the length of ๐ธ๐น on triangle ๐ธ๐ท๐น would be congruent with the length ๐ด๐ต on
triangle ๐ด๐ต๐ถ. ๐ด๐ต is given as 2.2 units, so ๐ธ๐น
will also be the same length, 2.2 units long.
In the final part of this question,
we need to work out the measure of angle ๐ท๐ธ๐น in triangle ๐ธ๐น๐ท. Once again, we could use the
congruency relationship to find the angle of ๐ท๐ธ๐น which must be congruent to angle
๐ถ๐ด๐ต in triangle ๐ด๐ต๐ถ. Weโre given on the diagram that
angle ๐ถ๐ด๐ต is 63.4 degrees. Therefore, angle ๐ท๐ธ๐น will also
be 63.4 degrees.
As an aside, sometimes in exam
questions weโre given two pairs of congruent angles and asked to work out a third
angle. But remember that we can apply the
fact that the sum of the angles in a triangle is 180 degrees to find any missing
angles in this situation. In this question, however, we can
give our answers as 4.5, 2.2, and 63.4 degrees.
