Video Transcript
Is the triangle 𝐴𝐵𝐶
isosceles?
We can recall that an isosceles
triangle is defined as a triangle that has two congruent sides. And because of the isosceles
triangle theorem, we know that isosceles triangles also have two congruent
angles. These base angles will be opposite
the congruent sides. We can prove that a triangle is
isosceles either by showing that a triangle has two congruent sides or by showing
that it has two congruent angles. If we look at the figure, we have
some information about the angles. So let’s see what we can work
out.
Firstly, we have the straight line
𝐶𝐷, and we are given that the measure of angle 𝐴𝐵𝐷 is 142 degrees. We can work out the measure of
angle 𝐴𝐵𝐶 by recalling that the angle measures on a straight line sum to 180
degrees. So the measure of angle 𝐴𝐵𝐶 is
equal to 180 degrees minus 142 degrees, which is 38 degrees.
Now we have two angle measures in
the triangle, we can work out the third angle by using the property that the
internal angle measures in a triangle sum to 180 degrees. So, we have 38 degrees plus 83
degrees plus the measure of angle 𝐴𝐶𝐵 is equal to 180 degrees. Simplifying, we have 121 degrees
plus the measure of angle 𝐴𝐶𝐵 is 180 degrees. And subtracting 121 degrees from
both sides, we have that the measure of angle 𝐴𝐶𝐵 is 59 degrees. Therefore, this triangle has angles
of 38 degrees, 59 degrees, and 83 degrees. There are no congruent angle
measures.
So, we can give the answer to the
question “Is the triangle 𝐴𝐵𝐶 isosceles?” as no, since we have proved that it
does not have two congruent angles.
