Video Transcript
In the figure, triangle 𝐴𝐵𝐶 and
triangle 𝐸𝐹𝐷 are congruent. Work out the length of 𝐵𝐶. Work out the length of 𝐸𝐹. Work out the measure of angle
𝐷𝐸𝐹.
In this question, we’ve got two
triangles, triangle 𝐴𝐵𝐶 and triangle 𝐸𝐹𝐷. We’re told that these two triangles
are congruent, which means that they’re the same shape and size. Even if they’re in a different
orientation, corresponding angles will be equal and corresponding pairs of sides
will be equal. In the first part of this question,
we’re asked to work out the length of 𝐵𝐶. So let’s see if we can find the
corresponding side in the other triangle 𝐸𝐹𝐷 to work out the length.
In some diagrams, it’s 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 𝐴𝐵𝐶
is congruent to triangle 𝐸𝐹𝐷. So that means if we’re looking at
the line 𝐵𝐶 in triangle 𝐴𝐵𝐶, then it would be congruent with the line 𝐹𝐷 on
triangle 𝐸𝐹𝐷. That’s because in a congruency
relationship, the order of the letters is very important. On our diagram, we’re given that
the length of 𝐹𝐷 is 4.5. Therefore, the length of 𝐵𝐶 must
also be 4.5. And so our answer for the first
part of the question is that 𝐵𝐶 is 4.5 units long.
Let’s look at the second
question. Here, we’re asked to find the
length of 𝐸𝐹 on triangle 𝐸𝐷𝐹. Using the congruency relationship,
the length of 𝐸𝐹 on triangle 𝐸𝐷𝐹 would be congruent with the length 𝐴𝐵 on
triangle 𝐴𝐵𝐶. 𝐴𝐵 is given as 2.2 units, so 𝐸𝐹
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 𝐷𝐸𝐹 in triangle 𝐸𝐹𝐷. Once again, we could use the
congruency relationship to find the angle of 𝐷𝐸𝐹 which must be congruent to angle
𝐶𝐴𝐵 in triangle 𝐴𝐵𝐶. We’re given on the diagram that
angle 𝐶𝐴𝐵 is 63.4 degrees. Therefore, angle 𝐷𝐸𝐹 will also
be 63.4 degrees.
As an aside, sometimes in exam
questions we’re 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.
