### Video Transcript

Is the triangle π΄π΅πΆ
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 letβs see what we can work
out.

Firstly, we have the straight line
πΆπ·, and we are given that the measure of angle π΄π΅π· is 142 degrees. We can work out the measure of
angle π΄π΅πΆ by recalling that the angle measures on a straight line sum to 180
degrees. So the measure of angle π΄π΅πΆ 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 π΄πΆπ΅ is equal to 180 degrees. Simplifying, we have 121 degrees
plus the measure of angle π΄πΆπ΅ is 180 degrees. And subtracting 121 degrees from
both sides, we have that the measure of angle π΄πΆπ΅ 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 βIs the triangle π΄π΅πΆ isosceles?β as no, since we have proved that it
does not have two congruent angles.